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Dissertations / Theses on the topic 'Homotopy'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

GrbicÌ, Jelena. "Universal homotopy associative, homotopy commutative H-spaces." Thesis, University of Aberdeen, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401586.

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For any connected space <i>X</i> the James construction shows that Ω<span style='font-family:Symbol'>S<i>X</i> is universal in the category of homotopy associative <i>H</i>-spaces in the sense that any map <i>f</i>: <i>X </i><i><span style='font-family:Symbol'>® Y </i>to a homotopy associative <i>H</i>-space factors through a uniquely determined H-map. Let <i>p</i> be a fixed prime number, and <i>X</i> a space localised at <i>p</i>. We study the possibility of generating a universal space <i>U(X)</i> from <i>X</i> which is universal in the category of homotopy associative, homotopy commutativ

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2

Saleh, Bashar. "Formality and homotopy automorphisms in rational homotopy theory." Licentiate thesis, Stockholms universitet, Matematiska institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-160835.

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This licentiate thesis consists of two papers treating subjects in rational homotopy theory. In Paper I, we establish two formality conditions in characteristic zero. We prove that adg Lie algebra is formal if and only if its universal enveloping algebra is formal. Wealso prove that a commutative dg algebra is formal as a dg associative algebra if andonly if it is formal as a commutative dg algebra. We present some consequences ofthese theorems in rational homotopy theory. In Paper II, we construct a differential graded Lie model for the universal cover of the classifying space of the grouplik

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3

Rehmeyer, Julie. "Homotopy colimits." Thesis, Massachusetts Institute of Technology, 1997. http://hdl.handle.net/1721.1/42605.

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4

Szumiło, Karol [Verfasser]. "Two Models for the Homotopy Theory of Cocomplete Homotopy Theories / Karol Szumiło." Bonn : Universitäts- und Landesbibliothek Bonn, 2014. http://d-nb.info/1238687156/34.

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5

Fleming, Thomas R. "Generalized link homotopy invariants." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3208096.

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Thesis (Ph. D.)--University of California, San Diego, 2006.<br>Title from first page of PDF file (viewed June 2, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 72-75).

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6

Wang, Guozhen Ph D. Massachusetts Institute of Technology. "Unstable chromatic homotopy theory." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99321.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 57-58).<br>In this thesis, I study unstable homotopy theory with chromatic methods. Using the v, self maps provided by the Hopkins-Smith periodicity theorem, we can decompose the unstable homotopy groups of a space into its periodic parts, except some lower stems. For fixed n, using the Bousfield-Kuhn functor [Phi]n, we can associate to any space a spectrum, which captures the vo-periodic part of its homotopy groups. I st

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7

Beke, Tibor 1970. "Homotopy theory and topoi." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/47465.

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8

Douglas, Christopher L. "Twisted stable homotopy theory." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33095.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.<br>Includes bibliographical references (p. 133-137).<br>There are two natural interpretations of a twist of stable homotopy theory. The first interpretation of a twist is as a nontrivial bundle whose fibre is the stable homotopy category. This kind of radical global twist forms the basis for twisted parametrized stable homotopy theory, which is introduced and explored in Part I of this thesis. The second interpretation of a twist is as a nontrivial bundle whose fibre is a particular element in the stable homoto

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9

Quirin, Kevin. "Lawvere-Tierney sheafification in Homotopy Type Theory." Thesis, Nantes, Ecole des Mines, 2016. http://www.theses.fr/2016EMNA0298/document.

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Le but principal de cette thèse est de définir une extension de la traduction de double-négation de Gödel à tous les types tronqués, dans le contexte de la théorie des types homotopique. Ce but utilisera des théories déjà existantes, comme la théorie des faisceaux de Lawvere-Tierney, quenous adapterons à la théorie des types homotopiques. En particulier, on définira le fonction de faisceautisation de Lawvere-Tierney, qui est le principal théorème présenté dans cette thèse.Pour le définir, nous aurons besoin de concepts soit déjà définis en théorie des types, soit non existants pour l’instant.

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10

Su, Zhixu. "Rational homotopy type of manifolds." [Bloomington, Ind.] : Indiana University, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3378383.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2009.<br>Title from PDF t.p. (viewed on Jul 9, 2010). Source: Dissertation Abstracts International, Volume: 70-10, Section: B, page: 6263. Adviser: James F. Davis.

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11

Yurasovskaya, Ekaterina. "Homotopy string links over surfaces." Thesis, University of British Columbia, 2008. http://hdl.handle.net/2429/2747.

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In his 1947 work "Theory of Braids" Emil Artin asked whether the braid group remained unchanged when one considered classes of braids under linkhomotopy, allowing each strand of a braid to pass through itself but not through other strands. We generalize Artin's question to string links over orientable surface M and show that under link-homotopy surface string links form a group PBn(M), which is isomorphic to a quotient of the surface pure braid group PBn(M). Surface braid groups and their properties are an area of active research by González-Meneses, Paris and Rolfsen, Goçalves and Guaschi, an

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12

Klaus, Michele. "Group actions on homotopy spheres." Thesis, University of British Columbia, 2011. http://hdl.handle.net/2429/35981.

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In the first part of the thesis we discuss the rank conjecture of Benson and Carlson. In particular, we prove that if G is a finite p-group of rank 3 and with p odd, or if G is a central extension of abelian p-groups, then there is a free finite G-CW-complex homotopy equivalent to the product of rk(G) spheres; where rk(G) is the rank of G. We also treat an extension of the rank conjecture to groups of finite virtual cohomological dimension. In this context, for p a fixed odd prime, we show that there is an infinite group L satisfying the two following properties: every finite subgroup G<L is

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13

Heggie, Murray. "Tensor products in homotopy theory." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=72792.

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14

Manin, Fedor. "Asymptotic invariants of homotopy groups." Thesis, The University of Chicago, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3712650.

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<p> We study the homotopy groups of a finite CW complex <i>X</i> via constraints on the geometry of representatives of their elements. For example, one can measure the “size” of α ∈ π<i> n</i> (<i>X</i>) by the optimal Lipschitz constant or volume of a representative. By comparing the geometrical structure thus obtained with the algebraic structure of the group, one can define functions such as growth and distortion in π<i>n</i>(<i>X</i>), analogously to the way that such functions are studied in asymptotic geometric group theory.</p><p> We provide a number of ex

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15

Antolini, Rosa. "Cubical structures and homotopy theory." Thesis, University of Warwick, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338578.

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16

Rego, E. "Characterizations of homotopy 3-spheres." Thesis, University of Warwick, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384786.

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17

Hollander, Sharon Joy 1975. "A homotopy theory for stacks." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8637.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.<br>Includes bibliographical references (p. 69-70).<br>We give a homotopy theoretic characterization of stacks on a site C which allows one to think of stacks as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category, that is a formal homotopy theory, in which stacks play the special role of the fibrant objects. This allows us to compare the different definitions of stacks and show that they lead to Quillen equivalent model categories. In addition, these model structur

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18

Ochi, Yoshihiro. "Iwasawa modules via homotopy theory." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624327.

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19

Miller, David. "Homotopy theory for stratified spaces." Thesis, University of Aberdeen, 2010. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=158352.

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There are many different notions of stratified spaces. This thesis concerns homotopically stratified spaces. These were defined by Frank Quinn in his paper Homotopically Stratified Sets ([16]). His definition of stratified space is very general and relates strata by “homotopy rather than geometric conditions”. This makes homotopically stratified spaces the ideal class of stratified spaces on which to define and study stratified homotopy theory. In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those

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20

Maunder, James. "Homotopy theory of moduli spaces." Thesis, Lancaster University, 2017. http://eprints.lancs.ac.uk/88429/.

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This thesis gathers three papers written by the author during PhD study at Lancaster University. In addition to these three papers, this thesis also contains two complementary sections. These two complementary sections are an introduction and a conclusion. The introduction discusses some recurring themes of the thesis and parts of the history leading to those results proven herein. The conclusion briefly comments on the outcomes of the research, its place in the current mathematical literature, and explores possibilities for further research. A common theme of this thesis is the study of Maure

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21

Bartels, Arthur C. "Link homotopy in codimension two /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9936836.

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22

Ge, Yuzhen. "Homotopy algorithms for the H² and the combined H²/H[infinity] model order reduction problems /." This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-09292009-020303/.

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Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1993.<br>On t.p. "[infinity]" appears as the infinity symbol and is superscript. Vita. Abstract. Includes bibliographical references (leaves 51-54). Also available via the Internet.

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23

Silva, Luciana Vale. "Teoria de homotopia simples e torção de Whitehead." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-18062007-143128/.

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Este trabalho apresenta a teoria de homotopia simples, desenvolvida por J. H. C. Whitehead, com o objetivo de obter um método para classificar espaços com o mesmo tipo de homotopia. Com esta motivação, Whitehead introduz o conceito de equivalência de homotopia simples entre complexos simpliciais, que posteriormente é generalizado para complexos CW, espaços criados pelo próprio Whitehead. Um resultado imediato desta teoria é que quando dois espaços têm o mesmo tipo de homotopia simples, eles têm o mesmo tipo de homotopia. A recíproca desta afirmação é então conjecturada. Mostraremos que trata-s

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24

Decker, Marvin Glen. "Loop spaces in motivic homotopy theory." [College Station, Tex. : Texas A&M University, 2006. http://hdl.handle.net/1969.1/ETD-TAMU-1808.

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25

Angelo, Maria Cristina. "The Gromov weak homotopy equivalence principle." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13525/.

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The h-principle is a general homotopic way to solve partial differential equations and, more generally, partial differential relations. The theory was started by Y. Eliashberg, M. Gromov and A. V. Philips and it allows one to reduce a differential topological problem to an algebraic topological problem. A way to prove the h-principle is by Convex Integration Theory. Developed originally by Gromov, it is applied to solve relations in jet spaces, including certain classes of undetermined non-linear systems of partial differential equations. The h-principle occurs for instance in immersion prob

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26

Zanardini, Aline. "Dirac structures and their homotopy classification." reponame:Repositório Institucional da UFPR, 2016. http://hdl.handle.net/1884/46204.

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Orientador : Prof. Dr. Llohann Sperança Dallagnol<br>Coorientador : Prof. Dr. Alexei Kotov<br>Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Matemática. Defesa: Curitiba, 07/09/2016<br>Inclui referências : f. 75-76<br>Área de concentração<br>Resumo: Nesta dissertação estamos interessados em estudar estruturas de Dirac. Nosso objetivo maior é classificá-las por homotopia. Para tal, começamos apresentando o formalismo básico da geometria generalizada. Primeiro introduzimos a contraparte linear e então passamos para variedades, onde

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27

Clarkson, James Price. "Group actions on finite homotopy spheres." Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/27134.

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Recently, Grodal and Smith [7}have developed a finite algebraic model to study hG-spaces where G is a finite group. The procedure associates to each G-space X with finite F_p homology a perfect chain complex of functors over the orbit category. When X has the homotopy type of a sphere, this construction is particularly well behaved. The reverse construction, building an hG-space from the algebraic model, generally produces an infinite dimensional space. In this thesis, we construct a finiteness obstruction for hG-spheres working one prime at a time. We then begin the development of a global

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28

Ehlers, Philip John. "Algebraic homotopy in simplicially enriched groupoids." Thesis, Bangor University, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.332384.

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29

Al, Shumrani Mohammed Ahmed Musa. "Homotopy theory in algebraic derived categories." Thesis, University of Glasgow, 2006. http://theses.gla.ac.uk/1905/.

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In this thesis, we introduce some new notions in the derived category D+(fg) (R) of bounded below chain complexes of finite type over local commutative noetherian ring R with maximal ideal m and residue field K in chapter three and study their relations to each other. Also, we set up the Adams spectral sequence for chain complexes in D+(f,g) (R) in chapter four and study its convergence. To accomplish this task, we give two background chapters. We give some good account of chain complexes in chapter one. We review some basic homological algebra and give definition and basic properties of chain

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30

Adams-Florou, Spiros. "Homeomorphisms, homotopy equivalences and chain complexes." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/6250.

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This thesis concerns the relationship between bounded and controlled topology and in particular how these can be used to recognise which homotopy equivalences of reasonable topological spaces are homotopic to homeomorphisms. Let f : X → Y be a simplicial map of finite-dimensional locally finite simplicial complexes. Our first result is that f has contractible point inverses if and only if it is an ε- controlled homotopy equivalences for all ε > 0, if and only if f × id : X × R → Y × R is a homotopy equivalence bounded over the open cone O(Y +) of Pedersen and Weibel. The most difficult part, t

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31

Raptis, Georgios. "Cobordism categories and abstract homotopy theory." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.510210.

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32

Hoyer, Rolf. "Two topics in stable homotopy theory." Thesis, The University of Chicago, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3627837.

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<p> We give a definition of a norm functor from <i>H</i>-Mackey functors to <i>G</i>-Mackey functors for <i>G</i> a finite group and <i>H</i> a subgroup of <i>G</i>. We check that this agrees with the construction of Mazur in the case <i>G</i> cyclic of prime power order and also with the topological definition of norm, which has an algebraic presentation due to Ullman. We then use this norm functor to give a characterization of Tambara functors as monoids of an appropriate flavor. </p><p> The second chapter is part of a joint project with Andrew Baker. We consider what happens when we t

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33

Burford, Jette Inger. "Homotopy implies isotopy for some orbifolds." Thesis, University of Liverpool, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329449.

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34

Vallejo, L. C. "Some homotopy properties of classical links." Thesis, University of Sussex, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377060.

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35

Lee, Wai Kei Peter. "Gröbner bases in rational homotopy theory." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/43786.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>Includes bibliographical references (leaves 38-39).<br>The Mayer-Vietoris sequence in cohomology has an obvious Eckmann-Hilton dual that characterizes the homotopy of a pullback, but the Eilenberg-Moore spectral sequence has no dual that characterizes the homotopy of a pushout. The main obstacle is the lack of an Eckmann-Hilton dual to the Kiinneth theorem with which to understand the homotopy of a coproduct. This difficulty disappears when working rationally, and we dualize Rector's construction of the Eile

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36

Haydon, James Henri. "Étale homotopy sections of algebraic varieties." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:88019ba2-a589-4179-ad7f-1eea234d284c.

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We define and study the fundamental pro-finite 2-groupoid of varieties X defined over a field k. This is a higher algebraic invariant of a scheme X, analogous to the higher fundamental path 2-groupoids as defined for topological spaces. This invariant is related to previously defined invariants, for example the absolute Galois group of a field, and Grothendieck’s étale fundamental group. The special case of Brauer-Severi varieties is considered, in which case a “sections conjecture” type theorem is proved. It is shown that a Brauer-Severi variety X has a rational point if and only if its étale

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37

Kraus, Nicolai. "Truncation levels in homotopy type theory." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/28986/.

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Homotopy type theory (HoTT) is a branch of mathematics that combines and benefits from a variety of fields, most importantly homotopy theory, higher dimensional category theory, and, of course, type theory. We present several original results in homotopy type theory which are related to the truncation level of types, a concept due to Voevodsky. To begin, we give a few simple criteria for determining whether a type is 0-truncated (a set), inspired by a well-known theorem by Hedberg, and these criteria are then generalised to arbitrary n. This naturally leads to a discussion of functions that ar

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38

Eklund, David. "Algebraic C*-actions and homotopy continuation." Licentiate thesis, Stockholm : Engineering sciences, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9380.

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Silva, Júnior João Alves. "First steps in homotopy type theory." Universidade Federal de Pernambuco, 2014. https://repositorio.ufpe.br/handle/123456789/13853.

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Submitted by Natalia de Souza Gonçalves (natalia.goncalves@ufpe.br) on 2015-05-08T13:12:46Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertation.pdf: 1398032 bytes, checksum: ba6c27cf093110dd1dcf9fea1b529c41 (MD5)<br>Made available in DSpace on 2015-05-08T13:12:46Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) dissertation.pdf: 1398032 bytes, checksum: ba6c27cf093110dd1dcf9fea1b529c41 (MD5) Previous issue date: 2014-02-27<br>CNPq<br>Em abril de 2013, o Programa de Fundamentos Unival

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CIOFFO, CIPRIANO JUNIOR. "HOMOTOPY SETOIDS AND GENERALIZED QUOTIENT COMPLETION." Doctoral thesis, Università degli Studi di Milano, 2022. http://hdl.handle.net/2434/933293.

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In this thesis, we deal with some categorical structures arising from the Martin-Löf Intuitionistic Type Theory. In the first part, we introduce the homotopy setoids, considering ideas from the homotopy type theory, and we study their categorical properties. In order to do that, we use the categorical framework of the elementary doctrines introduced by Maietti and Rosolini. In this setting, we provide some results about the elementary quotient completion and we prove that homotopy setoids form a weak notion of pretopos. In the second part of this thesis, we introduce the notion of biased eleme

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Graff, Emmanuel. ""Link-homotopy" in low dimensional topology." Electronic Thesis or Diss., Normandie, 2023. http://www.theses.fr/2023NORMC244.

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Ce mémoire explore la topologie de basse dimension, en mettant l'accent sur la théorie des nœuds. Une théorie consacrée à l'étude des nœuds tels qu'ils sont communément compris : des morceaux de ficelle enroulés dans l'espace ou, de manière plus générale, des entrelacs formés en prenant plusieurs bouts de ficelle. Les nœuds et les entrelacs sont étudiés à déformation près, par exemple, à isotopie près, ce qui implique des manipulations sans couper ni faire passer la ficelle à travers elle-même. Cette thèse explore la link-homotopie, une relation d'équivalence plus souple où des composantes dis

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Dubut, Jérémy. "Directed homotopy and homology theories for geometric models of true concurrency." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLN032/document.

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Le but principal de la topologie algébrique dirigée est d’étudier des systèmes qui évoluent avec le temps à travers leur géométrie. Ce sujet émergea en informatique, plus particulièrement en vraie concurrence, où Pratt introduisit les automates de dimension supérieure (HDA) en 1991 (en réalité, l’idée de la géométrie de la concurrence peut être retracée jusque Dijkstra en 1965). Ces automates sont géométriques par nature: chaque ensemble de n processus exécutant des actions indépendantes en parallèle peuvent être modélisées par un cube de dimension n, et un tel automate donne naissance à un es

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43

Junior, Luiz Roberto Hartmann. "Homotopia simples e classificação dos espaços lenticulares." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-03052007-104226/.

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Fizemos uma apresentação detalhada, com um enfoque geométrico, da Teoria de Homotopia Simples e como aplicação, uma análise detalhada da classificação por homotopia e homotopia simples dos Espaços Lenticulares<br>We made a detailed presentation, with a geometric approach, of Simple Homotopy Theory and as a major application we present a detailed analysis of homotopy and simple homotopy classification of Lens Spaces

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44

Dunlavy, Daniel Michael. "Homotopy optimization methods and protein structure prediction." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/2882.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.<br>Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Bani-Hashemian, Mohammad Hossein. "Projections of Immersed Surfaces and Regular Homotopy." Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-110697.

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<p>This thesis is based on U. Pinkall’s study of the classification of immersions of compact surfaces into R<sup>3</sup> up to regular homotopy. The main idea of the classification is to associate to any immersion f a quadratic form q<sub>f</sub> on the first homology group of the underlying surface Σ with Z<sub>2</sub> coefficients, whose associated bilinear form is the nondegenerate intersection form in H<sub>1</sub>(Σ,Z<sub>2</sub>), having the property that it depends only on the regular homotopy class of f. In the case of orientable surfaces q<sub>f</sub> turns out to be a Z<sub>2</sub>-q

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Ali, Seema. "Colouring generalized Kneser graphs and homotopy theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0014/MQ34938.pdf.

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Chakraborty, Amal. "Parallel homotopy curve tracking on a hypercube." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-09162005-115011/.

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48

Gupta, Neha. "Homotopy quantum field theory and quantum groups." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/38110/.

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The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf

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Pinzon, Daniel F. "VERTEX ALGEBRAS AND STRONGLY HOMOTOPY LIE ALGEBRAS." UKnowledge, 2006. http://uknowledge.uky.edu/gradschool_diss/382.

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Vertex algebras and strongly homotopy Lie algebras (SHLA) are extensively used in qunatum field theory and string theory. Recently, it was shown that a Courant algebroid can be naturally lifted to a SHLA. The 0-product in the de Rham chiral algebra has an identical formula to the Courant bracket of vector fields and 1-forms. We show that in general, a vertex algebra has an SHLA structure and that the de Rham chiral algebra has a non-zero l4 homotopy.

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50

Hellstrøm-Finnsen, Magnus. "The Homotopy Theory of (∞,1)-Categories." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-24362.

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The homotopy category of a stable (&#8734;,1)-category can be endowed with a triangulated structure. The main objective of this thesis is to give a proof of this fact. First it will be discussed some ideas of higher category theory, before (&#8734;,1)-categories and models of (&#8734;,1)-categories will be studied. In particular, topological categories and simplicial categories will be mentioned, but the main focus will be on quasi-categories, which all are models for (&#8734;,1)-categories. The theory of (&#8734;,1)-categories, which is required in order to define stable (

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