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Rozprawy doktorskie na temat „Ergodic and geometric group theory”

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Data publikacji: 31 sierpnia 2024

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1

Cannizzo, Jan. "Schreier Graphs and Ergodic Properties of Boundary Actions." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31444.

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This thesis is broadly concerned with two problems: investigating the ergodic properties of boundary actions, and investigating various properties of Schreier graphs. Our main result concerning the former problem is that, in a variety of situations, the action of an invariant random subgroup of a group G on a boundary of G (e.g. the hyperbolic boundary, or the Poisson boundary) is conservative (there are no wandering sets). This addresses a question asked by Grigorchuk, Kaimanovich, and Nagnibeda and establishes a connection between invariant random subgroups and normal subgroups. We approach

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2

Long, Yusen. "Diverse aspects of hyperbolic geometry and group dynamics." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM016.

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Cette thèse explore divers sujets liés à la géométrie hyperbolique et à la dynamique de groupes, dans le but d'étudier l'interaction entre la géométrie et la théorie de groupes. Elle couvre un large éventail de disciplines mathématiques, telles que la géométrie convexe, l'analyse stochastique, la théorie ergodiques et géométriques de groupes, et la topologie en basses dimensions, et cætera. Comme résultats de recherche, la géométrie hyperbolique des corps convexes en dimension infinie est examinée en profondeur, et des tentatives sont faites pour développer la géométrie intégrale en dimension

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3

Benson, Martin. "Topics in geometric group theory." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.428957.

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4

Williams, Benjamin Thomas. "Two topics in geometric group theory." Thesis, University of Southampton, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323942.

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5

Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial exa

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6

Ashdown, M. A. J. "Geometric algebra, group theory and theoretical physics." Thesis, University of Cambridge, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.596181.

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This dissertation applies the language of geometric algebra to group theory and theoretical physics. Geometric algebra, which is introduced in Chapter 2, provides a natural extension of the concept of multiplication from real numbers to geometric objects such as line segments and planes. It is based on Clifford algebra and augmented by auxiliary definitions which give it a geometric interpretation. Since geometric algebra provides a natural encoding of the concepts of directed quantities, it has the potential to unify many of the disparate systems of notation that are used in mathematics. In C

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7

Gill, Olivia Jo. "Geometric and homological methods in group theory : constructing small group resolutions." Thesis, London Metropolitan University, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.573402.

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Given two groups K and H for which we have the free crossed resolutions, B* ɛ K and C* ɛ H respectively. Our aim is to construct a free crossed resolution, A* ɛ G, by way of induction on the degree n, for any semidirect product G = K ><I H. First we show how to find a set ZI of generators for the free group Al and the corresponding unique epimorphism from the free group on those generators to the semidirect product. This gives us the l-dimensional free crossed resolution A1 ɛ G, (see Proposition 4.1). Next we define a set of generators Z2 that together with Z1, constitute a gener- ating se

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8

Joubert, Paul. "Geometric actions of the absolute Galois group." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/2508.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2006.<br>This thesis gives an introduction to some of the ideas originating from A. Grothendieck's 1984 manuscript Esquisse d'un programme. Most of these ideas are related to a new geometric approach to studying the absolute Galois group over the rationals by considering its action on certain geometric objects such as dessins d'enfants (called stick figures in this thesis) and the fundamental groups of certain moduli spaces of curves. I start by defining stick figures and explaining the connection between these innocent combinatoria

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9

El-Mosalamy, Mohamed Soliman Hassan. "Applications of star complexes in group theory." Thesis, University of Glasgow, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293464.

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10

Fennessey, Eric James. "Some applications of geometric techniques in combinatorial group theory." Thesis, University of Glasgow, 1989. http://theses.gla.ac.uk/6159/.

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Combinatorial group theory abounds with geometrical techniques. In this thesis we apply some of them to three distinct areas. In Chapter 1 we present all of the techniques and background material neccessary to read chapters 2,3,4. We begin by defining complexes with involutary edges and define coverings of these. We then discuss equivalences between complexes and use these in §§1.3 and 1.4 to give a way (the level method) of simplifying complexes and an application of this method (Theorem 1.3). We then discuss star-complexes of complexes. Next we present background material on diagrams and pic

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11

Bergeron, Maxime. "On CAT(0) aspects of geometric group theory and some applications to geometric superrigidity." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=110571.

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Since their popularization by Gromov in the eighties, CAT(0) metric spaces of bounded curvature as defined by Alexandrov have been the locus of great progress in infinite group theory. Surveying ideas and constructions of geometric group theory, we express a bias towards groups acting on structures of this kind. As such, swiftly acquainting the reader with the theory of CAT(0) spaces, we provide a variety of examples obtained by gluing together families of convex polyhedra along their isometric faces. In this context, Gromov's link condition provides a local-to-global framework for non-positiv

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12

Jarrett, Kieran. "Non-singular actions of countable groups." Thesis, University of Bath, 2018. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.761021.

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In this thesis we study actions of countable groups on measure spaces underthe assumption that the dynamics are non-singular, with particular reference topointwise ergodic theorems and their relationship to the critical dimensions ofthe action.

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13

Bavuma, Yanga. "Some combinatorial aspects in algebraic topology and geometric group theory." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29763.

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The present Msc thesis deals with classical topics of topology and it has been written, referring to [C. Kosniowski, Introduction to Algebraic Topology, Cambridge University Press, 1980, Cambridge], which is a well known textbook of algebraic topology. It has been selected a list of main exercises from this reference, whose solutions were not directly available, or subject to differerent methods. In fact combinatorial methods have been preferred and the result is a self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems i

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14

Davidson, Peter John. "Geometric methods in the study of Pride groups and relative presentations." Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/230/.

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Thesis (Ph.D.) - University of Glasgow, 2008.<br>Ph.D. thesis submitted to the Faculty of Information and Mathematical Sciences, Department of Mathematics, University of Glasgow, 2008. Includes bibliographical references. Print version also available.

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15

Sathaye, Bakul Sathaye. "Obstructions to Riemannian smoothings of locally CAT(0) manifolds." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1531416481628579.

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16

Atanasov, Risto. "Groups of geometric dimension 2." Diss., Online access via UMI:, 2007.

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17

Cotton-Barratt, Owen. "Geometric and profinite properties of groups." Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.572875.

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We use profinite Bass-Serre theory (the theory of profinite group actions on profinite trees) to prove that the fundamental groups of finite graphs of free groups which are l-acylindrical and have finitely generated edge groups are conjugacy separable. We apply this theorem to: demonstrate that a generic positive one-relator group is conjugacy separable; produce a variant of the Rips con- struction in which the output group is conjugacy separable; apply this last to exhibit an example of a strong profinite equivalence between two finitely presented groups, one of which is conjugacy separable a

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18

Genevois, Anthony. "Cubical-like geometry of quasi-median graphs and applications to geometric group theory." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0569/document.

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La classe des graphes quasi-médians est une généralisation des graphes médians, ou de manière équivalente, des complexes cubiques CAT(0). L'objectif de cette thèse est d'introduire ces graphes dans le monde de la théorie géométrique des groupes. Dans un premier temps, nous étendons la notion d'hyperplan définie dans les complexes cubiques CAT(0), et nous montrons que la géométrie d'un graphe quasi-médian se réduit essentiellement à la combinatoire de ses hyperplans. Dans la deuxième partie de notre texte, qui est le cœur de la thèse, nous exploitons la structure particulière des hyperplans pou

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19

Awang, Jennifer S. "Dots and lines : geometric semigroup theory and finite presentability." Thesis, University of St Andrews, 2015. http://hdl.handle.net/10023/6923.

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Geometric semigroup theory means different things to different people, but it is agreed that it involves associating a geometric structure to a semigroup and deducing properties of the semigroup based on that structure. One such property is finite presentability. In geometric group theory, the geometric structure of choice is the Cayley graph of the group. It is known that in group theory finite presentability is an invariant under quasi-isometry of Cayley graphs. We choose to associate a metric space to a semigroup based on a Cayley graph of that semigroup. This metric space is constructed by

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20

Gielen, Steffen C. M. "Geometric aspects of gauge and spacetime symmetries." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240578.

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We investigate several problems in relativity and particle physics where symmetries play a central role; in all cases geometric properties of Lie groups and their quotients are related to physical effects. The first part is concerned with symmetries in gravity. We apply the theory of Lie group deformations to isometry groups of exact solutions in general relativity, relating the algebraic properties of these groups to physical properties of the spacetimes. We then make group deformation local, generalising deformed special relativity (DSR) by describing gravity as a gauge theory of the de Sitt

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21

Sisto, Alessandro. "Geometric and probabilistic aspects of groups with hyperbolic features." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:bcf456c4-eef0-4fe8-bb7d-8b15f9cf7b18.

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The main objects of interest in this thesis are relatively hyperbolic groups. We will study some of their geometric properties, and we will be especially concerned with geometric properties of their boundaries, like linear connectedness, avoidability of parabolic points, etc. Exploiting such properties will allow us to construct, under suitable hypotheses, quasi-isometric embeddings of hyperbolic planes into relatively hyperbolic groups and quasi-isometric embeddings of relatively hyperbolic groups into products of trees. Both results have applications to fundamental groups of 3-manifolds. We

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22

Sercombe, Damian. "A family of uniform lattices acting on a Davis complex with a non-discrete set of covolumes." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/16026.

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Let (W,S) be a Coxeter system with Davis complex Σ. The polyhedral automorphism group G of Σ is a locally compact group under the compact-open topology. If G is a discrete group (as characterised by Haglund-Paulin), then the set Vu(G) of uniform lattices in G is discrete. Whether the converse is true remains an open problem. Under certain assumptions on (W,S), we show that Vu(G) is non-discrete and contains rationals (in lowest form) with denominators divisible by arbitrarily large powers of any prime less than a fixed integer. We explicitly construct our lattices as fundamental groups of comp

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23

Barrett, Benjamin James. "Detecting topological properties of boundaries of hyperbolic groups." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/285572.

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In general, a finitely presented group can have very nasty properties, but many of these properties are avoided if the group is assumed to admit a nice action by isometries on a space with a negative curvature property, such as Gromov hyperbolicity. Such groups are surprisingly common: there is a sense in which a random group admits such an action, as do some groups of classical interest, such as fundamental groups of closed Riemannian manifolds with negative sectional curvature. If a group admits an action on a Gromov hyperbolic space then large scale properties of the space give useful invar

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24

Solomyak, Margarita. "Essential spanning forests and electric networks in groups /." Thesis, Connect to this title online; UW restricted, 1997. http://hdl.handle.net/1773/5767.

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25

Kuckuck, Benno. "Finiteness properties of fibre products." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:a9624d17-9d11-4bd0-8c46-78cbba73469c.

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A group Γ is of type F<sub>n</sub> for some n ≥ 1 if it has a classifying complex with finite n-skeleton. These properties generalise the classical notions of finite generation and finite presentability. We investigate the higher finiteness properties for fibre products of groups.

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26

Cornwell, Christopher R. "On the Combinatorics of Certain Garside Semigroups." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.

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27

Cannas, Sonia. "Geometric representation and algebraic formalization of musical structures." Thesis, Strasbourg, 2018. http://www.theses.fr/2018STRAD047/document.

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Cette thèse présente des généralisations u groupe néo-riemannien PLR, que agit sur l'ensemble des 24 triades majeures et mineures. Le travail commence par une reconstruction de l'histoire de Tonnetz, un graphe associé aux trois transformations qui génèrent le groupe PLR. La thèse présente deux généralisations du groupe PLR pour les accords de septième. Le premier agit sur le tournage des septièmes de dominantes, mineure, semi-diminuée, majeure et diminuée, le second comprend également la septième mineure majeur, majeure augmenté, l'augmentée et la septième dedominante bémol. Nous avons égaleme

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28

Woodruff, Benjamin M. "Statistical Properties of Thompson's Group and Random Pseudo Manifolds." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd854.pdf.

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29

Carette, Mathieu. "The automorphism group of accessible groups and the rank of Coxeter groups." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210261.

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Cette thèse est consacrée à l'étude du groupe d'automorphismes de groupes agissant sur des arbres d'une part, et du rang des groupes de Coxeter d'autre part.<p><p>Via la théorie de Bass-Serre, un groupe agissant sur un arbre est doté d'une structure algébrique particulière, généralisant produits amalgamés et extensions HNN. Le groupe est en fait déterminé par certaines données combinatoires découlant de cette action, appelées graphes de groupes. <p><p>Un cas particulier de cette situation est celle d'un produit libre. Une présentation du groupe d'automorphisme d'un produit libre d'un nombre fi

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30

Gardam, Giles. "Encoding and detecting properties in finitely presented groups." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:0c8a7009-7e04-4f66-911b-298ad87061fb.

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In this thesis we study several properties of finitely presented groups, through the unifying paradigm of encoding sought-after group properties into presentations and detecting group properties from presentations, in the context of Geometric Group Theory. A group law is said to be detectable in power subgroups if, for all coprime m and n, a group G satisfies the law if and only if the power subgroups G(<sup>m</sup>) and G(<sup>n</sup>) both satisfy the law. We prove that for all positive integers c, nilpotency of class at most c is detectable in power subgroups, as is the k-Engel law for k at

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31

Bounds, Jordan. "On the quasi-isometric rigidity of a class of right-angled Coxeter groups." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1561561078356503.

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32

Lynch, Keith. "On triangles and quadrilaterals of groups." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/38574.

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This dissertation demonstrates the existence of a pair of algebraic and geometric structures on triangles of groups and on quadrilaterals of groups. These structures are an automatic and biautomatic structure. In addition, this paper also discusses the growth function for the quadrilaterals. We show that these groups have these desired structures and discuss what they are. We also give an extraordinary example of a pair of quadrilaterals of groups that are defined nearly identically but do not behave alike.<br>Ph. D.

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33

Sale, Andrew W. "The length of conjugators in solvable groups and lattices of semisimple Lie groups." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:ea21dab2-2da1-406a-bd4f-5457ab02a011.

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The conjugacy length function of a group Γ determines, for a given a pair of conjugate elements u,v ∈ Γ, an upper bound for the shortest γ in Γ such that uγ = γv, relative to the lengths of u and v. This thesis focuses on estimating the conjugacy length function in certain finitely generated groups. We first look at a collection of solvable groups. We see how the lamplighter groups have a linear conjugacy length function; we find a cubic upper bound for free solvable groups; for solvable Baumslag--Solitar groups it is linear, while for a larger family of abelian-by-cyclic groups we get either

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34

Lima, Francismar Ferreira 1985. "Pontos fixos por grupos finitos agindo sobre grupos solúveis de tipo FP infinito." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306924.

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Orientador: Dessislava Hristova Kochloukova<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-23T11:19:15Z (GMT). No. of bitstreams: 1 Lima_FrancismarFerreira_M.pdf: 2264816 bytes, checksum: 31f3b411247775dcde6338655fbd496b (MD5) Previous issue date: 2013<br>Resumo: O resumo poderá ser visualizado no texto completo da tese digital<br>Abstract: The complete Abstract is available with the full electronic document.<br>Mestrado<br>Matematica<br>Mestre em Matemática

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35

Shim, Sangho. "Large scale group network optimization." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31737.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.<br>Committee Chair: Ellis L. Johnson; Committee Member: Brady Hunsaker; Committee Member: George Nemhauser; Committee Member: Jozef Siran; Committee Member: Shabbir Ahmed; Committee Member: William Cook. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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36

Kelvey, Robert J. Kelvey. "Properties of groups acting on Twin-Trees and Chabauty space." Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1479423366082688.

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Disarlo, Valentina. "Combinatorial methods in Teichmüller theory." Doctoral thesis, Scuola Normale Superiore, 2013. http://hdl.handle.net/11384/85687.

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In this thesis we deal with combinatorial and geometric properties of arc complexes and triangulation graphs, and we will provide some applications to the study of the mapping class group and to the Teichmüller theory of a bordered surface. The thesis is divided into two parts. In the former we deal with the problem of combinatorial rigidity of arc complexes. In the latter we study some large-scale properties of the arc complex and the 1-skeleton of its dual, the so-called ideal triangulation graph.

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38

Almeida, Kisnney Emiliano de 1984. "Sobre os sigma-invariantes unidimensionais de grupos de Artin." [s.n.], 2012. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306925.

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Orientador: Dessislava Hristova Kochloukova<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-20T20:07:55Z (GMT). No. of bitstreams: 1 Almeida_KisnneyEmilianode_D.pdf: 833428 bytes, checksum: 3f425f5150e4ce7915c42d59f2a772be (MD5) Previous issue date: 2012<br>Resumo: A teoria de ?-invariantes surgiu do trabalho de Bieri e Strebel, que definiram o primeiro ?-invariante, apenas para grupos metabelianos, e o usaram para descrever os grupos metabelianos finitamente gerados [BiSt]. Posterior

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39

Yang, Ruotao. "Twisted Whittaker category on affine flags and category of representations of mixed quantum group." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0064.

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Supposons que G est un groupe reductif. Nous avons l’équivalence géométrique de Satake qui identifie Sph(G), les faisceau pervers G (O) équivalentes sur grassmannin affine en tant que catégorie de représentation dimensionnelle finie de H, le groupe duel de Langlands de G. Notez qu’il existe une équivalence : Whit(Gr) = Sph(G). Ici, Whit(Gr) est la catégorie de module D (N(K), \chi)-equivalent sur Gr. Maintenant, la catégorie de représentation admet une déformation par la catégorie des représentations de groupe quantique. Le côté gauche, nous pouvons considérer les D modules torsadé sur grassma

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Disarlo, Valentina. "Combinatorial methods in Teichmüller theory." Phd thesis, Université de Strasbourg, 2013. http://tel.archives-ouvertes.fr/tel-00875029.

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In this thesis we deal with combinatorial and geometric properties of arc complexes and triangulation graphs, and we will provide some applications to the study of the mapping class group and to the Teichmüller theory of a bordered surface. The thesis is divided into two parts. In the former we deal with the problem of combinatorial rigidity of arc complexes. In the latter we study some large-scale properties of the arc complex and the 1-skeleton of its dual, the so-called ideal triangulation graph.

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41

Maillot, Sylvain. "Quasi-isométries, groupes de surfaces et orbifolds fibrés de Seifert." Phd thesis, Université Paul Sabatier - Toulouse III, 2000. http://tel.archives-ouvertes.fr/tel-00001342.

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Le résultat principal est une caractérisation homotopique des orbifolds de dimension 3 qui sont fibrés de Seifert : si O est un orbifold de dimension 3 fermé, orientable et petit dont le groupe fondamental admet un sous-groupe infini cyclique normal, alors O est de Seifert. Ce théorème généralise un résultat de Scott, Mess, Tukia, Gabai et Casson-Jungreis pour les variétés. Il repose sur une caractérisation des groupes de surfaces virtuels comme groupes quasi-isométriques à un plan riemannien complet. D'autres résultats sur les quasi-isométries entre groupes et surfaces sont obtenus.

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42

Camelo, Botero Miguel Hernando. "A geometric routing scheme in word-metric spaces for data networks." Doctoral thesis, Universitat de Girona, 2014. http://hdl.handle.net/10803/283749.

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This research work explores the use of the Greedy Geometric Routing (GGR) schemes to solve the scalability problem of the routing systems in Internet-like networks and several families of Data Center architectures. We propose a novel and simple embedding of any connected finite graph into a Word-Metric space, i.e., a metric space generated by algebraic groups. Then, built on top of this greedy embedding, we propose three GGR schemes and we prove the theoretical upper bounds of the Routing Table size, vertex label size and stretch. The first scheme works for any kind of graph and the other two

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D'Andrea, Joy. "Fundamental Transversals on the Complexes of Polyhedra." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3746.

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We present a formal description of `Face Fundamental Transversals' on the faces of the Complexes of polyhedra (meaning threedimensional polytopes). A Complex of a polyhedron is the collection of the vertex points of the polyhedron, line segment edges and polygonal faces of the polyhedron. We will prove that for the faces of any 3-dimensional complex of a polyhedron under face adjacency relations, that a `Face Fundamental Transversal' exists, and it is a union of the connected orbits of faces that are intersected exactly once. While exploring the problem of finding a face fundamental transversa

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Silva, Leonardo de Amorin e. 1980. "Grupos abelianos-por-(nilpotentes de classe 2)." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306919.

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Orientador: Dessislava Hristova Kochloukova<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica<br>Made available in DSpace on 2018-08-26T02:25:15Z (GMT). No. of bitstreams: 1 Silva_LeonardodeAmorine_D.pdf: 582293 bytes, checksum: ed3c907af5279b8923c782d730bcf1d4 (MD5) Previous issue date: 2014<br>Resumo: Nesta tese consideramos uma extensão cindida G de um grupo abeliano A por um grupo nilpotente (de classe 2) Q e provamos dois resultados. Primeiro, se Q age nilpotentemente sobre A e G tem tipo FP2, calculamos o sigma invaria

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Nicol, Andrew. "Quasi-isometries of graph manifolds do not preserve non-positive curvature." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405894640.

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Dufloux, Laurent. "Dimension de Hausdorff des ensembles limites." Thesis, Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCD022/document.

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Soit G le groupe SO°(1, n) (n ≥ 3) ou PU(1, n) (n ≥ 2) et fixons une décomposition d'Iwasawa G = KAN. Soit ɼ un sous-groupe discret de G, que nous supposons Zariski-dense et de mesure de Bowen-Margulis-Sullivan finie. Lorsque G = SO°(1, n), nous étudions la géométrie de la mesure de Bowen-Margulis-Sullivan le long des sous-groupes fermés connexes de N, en lien avec la dichotomie de Mohammadi-Oh. Nous établissons des résultats déterministes sur la dimension des projections de la mesure de Patterson- Sullivan. Lorsque G = PU(1, n), nous relions la géométrie de la mesure de Bowen- Margulis-Sulliv

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Petersen, Willis L. "The Lie Symmetries of a Few Classes of Harmonic Functions." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd837.pdf.

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Bouette, Margot. "Sur la croissance des automorphismes des groupes de Baumslag-Soliltar." Thesis, Rennes 1, 2016. http://www.theses.fr/2016REN1S053/document.

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Un groupe de Baumslag-Solitar est un groupe dont la présentation est, pour p et q entiers non nuls. A chaque groupe de Baumslag-Solitar est associé un espace de déformation D p, q d'actions sur des arbres analogue à l'outre espace. Aut(BS(p, q)) agit sur cet espace ce qui induit une action du groupe des automorphismes extérieurs Out(BS(p,q)). Nous nous intéresserons au cas plus complexe où q est un multiple de p et dans un premier temps, nous démontrerons que tout automorphisme de BS(p, pn) est réductible ce qui signifie qu'il existe un BS(p,pn)-arbre T et une application laissant invariante u

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Bouljihad, Mohamed. "Propriété (T) de Kazhdan relative à l'espace." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEN010/document.

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L'objet de cette thèse est l'étude de la propriété (T) relative à l'espace (ou rigidité au sens de Popa) d'actions de groupes dénombrables sur des espaces de probabilité standards préservant une mesure de probabilité (pmp). Ces dix dernières années, la propriété (T) relative à l'espace a permis de résoudre de nombreux problèmes dans le cadre de la théorie ergodique des actions de groupes et des algèbres de von Neumann. Néanmoins, certains aspects théoriques de cette notion restent largement mystérieux. Une question encore ouverte consiste à déterminer les groupes admettant une action libre erg

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Vittone, Davide. "Submanifolds in Carnot groups." Doctoral thesis, Scuola Normale Superiore, 2006. http://hdl.handle.net/11384/85698.

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