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Relevant bibliographies by topics / Classes de homotopia

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Academic literature on the topic 'Classes de homotopia'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Classes de homotopia"

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Li, Bang-He, and Gui-Song Li. "Immersions with non-zero normal vector fields." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (1992): 281–85. http://dx.doi.org/10.1017/s0305004100070961.

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Let M be a smooth n-manifold, X be a smooth (2n − 1)-manifold, and g:M → X be a map. It was proved in [6] that g is always homotopic to an immersion. The set of homotopy classes of monomorphisms from TM into g*TX, which is denoted by Sg, may be enumerated either by the method of I. M. James and E. Thomas or by the singularity method of U. Koschorke (see [1] and references therein). When the natural action of π1(XM, g) on Sg is trivial, for example, if X is euclidean, the set Sg is in one-to-one correspondence with the set of regular homotopy classes of immersions homotopic to g (see e.g. [4]).

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Manuilov, V., and K. Thomsen. "Extensions of $C^*$-algebras and translation invariant asymptotic homomorphisms." MATHEMATICA SCANDINAVICA 100, no. 1 (2007): 131. http://dx.doi.org/10.7146/math.scand.a-15018.

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Let $A$, $B$ be $C^*$-algebras; $A$ separable, $B$ $\sigma$-unital and stable. We introduce a notion of translation invariance for asymptotic homomorphisms from $SA=C_0(\mathsf{R})\otimes A$ to $B$ and show that the Connes-Higson construction applied to any extension of $A$ by $B$ is homotopic to a translation invariant asymptotic homomorphism. In the other direction we give a construction which produces extensions of $A$ by $B$ out of such a translation invariant asymptotic homomorphism. This leads to our main result; that the homotopy classes of extensions coincide with the homotopy classes

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Penteado, Dirceu, and Thales Fernando Vilamaior Paiva. "Reidemeister classes for coincidences between sections of a fiber bundle." Boletim da Sociedade Paranaense de Matemática 38, no. 6 (2019): 85–97. http://dx.doi.org/10.5269/bspm.v38i6.37223.

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Let $s_0,f_0$ be two sections of a fiber bundle $q: E\to B$ and the coincidence set $\Gamma(s_0,f_0)\neq \emptyset$. We consider the following question: Is there $s_0\simeq_B s_1$ (by the homotopies which cover the constant homotopy $\overline{I}_B$ on the basic space) such that $\Gamma(s_1, f_0)=\emptyset$? If $b_0\in \Gamma(s_0,f_0)$ and $F_0=q^{-1}(b_0)$ is the typical fiber, in this context we can use the homotopy lifting extension propriety of the fibration $q$ to obtain homotopies over $B$. When we make this and the basic point are fixed we can use the elements $s_0(\beta), f_0(\beta^{-1

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Biasi, Carlos, Alice K. M. Libardi, Thiago de Melo, and Edivaldo L. dos Santos. "Some results on extension of maps and applications." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 6 (2019): 1465–72. http://dx.doi.org/10.1017/prm.2018.113.

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AbstractThis paper concerns extension of maps using obstruction theory under a non-classical viewpoint. It is given a classification of homotopy classes of maps and as an application it is presented a simple proof of a theorem by Adachi about equivalence of vector bundles. Also it is proved that, under certain conditions, two embeddings are homotopic up to surgery if and only if the respective normal bundles are SO-equivalent.

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COSTANTINO, FRANCESCO. "BRANCHED SHADOWS AND COMPLEX STRUCTURES ON 4-MANIFOLDS." Journal of Knot Theory and Its Ramifications 17, no. 11 (2008): 1429–54. http://dx.doi.org/10.1142/s0218216508006683.

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We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spinc-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

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Ito, Noboru, and Yusuke Takimura. "Strong and weak (1, 2, 3) homotopies on knot projections." International Journal of Mathematics 26, no. 09 (2015): 1550069. http://dx.doi.org/10.1142/s0129167x1550069x.

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A knot projection is an image of a generic immersion from a circle into a two-dimensional sphere. We can find homotopies between any two knot projections by local replacements of knot projections of three types, called Reidemeister moves. This paper defines an equivalence relation for knot projections called weak (1, 2, 3) homotopy, which consists of Reidemeister moves of type 1, weak type 2, and weak type 3. This paper defines the first nontrivial invariant under weak (1, 2, 3) homotopy. We use this invariant to show that there exist an infinite number of weak (1, 2, 3) homotopy equivalence c

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BYBERI, EVARIST, and VLADIMIR CHERNOV (TCHERNOV). "VIRTUAL BRIDGE NUMBER ONE KNOTS." Communications in Contemporary Mathematics 10, supp01 (2008): 1013–21. http://dx.doi.org/10.1142/s0219199708003137.

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We define the virtual bridge number vb (K) and the virtual unknotting number vu (K) invariants for virtual knots. For ordinary knots K they are closely related to the bridge number b(K) and the unknotting number u(K) and we have vu (K) ≤ u(K), vb(K) ≤ b(K). There are no ordinary knots K with b(K) = 1. We show there are infinitely many homotopy classes of virtual knots each of which contains infinitely many isotopy classes of K with vb (K) = 1. In fact for each i ∈ ℕ there exists K virtually homotopic (but not virtually isotopic) to the unknot with vb (K) = 1 and vu (K) = i.

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HUGHES, JAMES R. "FINITE TYPE LINK HOMOTOPY INVARIANTS OF k-TRIVIAL LINKS." Journal of Knot Theory and Its Ramifications 12, no. 03 (2003): 375–93. http://dx.doi.org/10.1142/s0218216503002524.

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In a recent paper [8], Xiao-Song Lin gave an example of a finite type invariant of links up to link homotopy that is not simply a polynomial in the pairwise linking numbers. Here we present a reformulation of the problem of finding such polynomials using the primary geometric obstruction homomorphism, previously used to study realizability of link group automorphisms by link homotopies. Using this reformulation, we generalize Lin's results to k-trivial links (links that become homotopically trivial when any k components are deleted). Our approach also gives a method for finding torsion finite

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Ito, Noboru, and Yusuke Takimura. "Positive knots and weak (1, 3) homotopy." Journal of Knot Theory and Its Ramifications 29, no. 09 (2020): 2050061. http://dx.doi.org/10.1142/s0218216520500613.

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It is known that there exists a surjective map from the set of weak (1, 3) homotopy classes of knot projections to the set of positive knots [N. Ito and Y. Takimura, (1, 2) and weak (1, 3) homotopies on knot projections, J. Knot Theory Ramifications 22 (2013) 1350085]. An interesting question whether this map is also injective, which question was formulated independently by S. Kamada and Y. Nakanishi in 2013 (Question q1). This paper obtains an answer to this question.

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Hempel, John. "One-relator surface groups." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (1990): 467–74. http://dx.doi.org/10.1017/s030500410006936x.

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For X a subset of a group G, the smallest normal subgroup of G which contains X is called the normal closure of X and is denoted by ngp (X; G) or simply by ngp (X) if there is no possibility of ambiguity. By a surface group we mean the fundamental group of a compact surface. We are interested in determining when a normal subgroup of a surface group contains a simple loop – the homotopy class of an embedding of S1 in the surface, or more generally, a power of a simple loop. This is significant to the study of 3-manifolds since a Heegaard splitting of a 3-manifold is reducible (cf. [2]) if and o

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Dissertations / Theses on the topic "Classes de homotopia"

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Andrade, Allan Edley Ramos de. "D-classes de homotopia, uma generalização da teoria de Δ-classes de homotopia." Universidade Federal de São Carlos, 2011. https://repositorio.ufscar.br/handle/ufscar/5872.

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Made available in DSpace on 2016-06-02T20:28:25Z (GMT). No. of bitstreams: 1 3473.pdf: 724122 bytes, checksum: 1383c01c677611f5c289fd137bc88597 (MD5) Previous issue date: 2011-03-04<br>Financiadora de Estudos e Projetos<br>This work is based on Ph.d. thesis of R.Brooks [1]. R.Brooks develops his work in three parts, first establishes Nielsen s theory (Essential class, Nielsen s number, estimates for the Nielsen s number) for determined classes of pairs of homotopy, called _-classes of homotopy. In the second part using homology and cohomology develop an index, that associates to each tuple (

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Melo, Thiago de. ""Enumeração dos fibrados vetoriais sobre superfícies fechadas"." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-13052005-193219/.

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O objetivo desse trabalho é fazer uma enumeração dos fibrados planos reais sobre algumas superfícies, como por exemplo, a esfera e o g-toro. Entre outras ferramentas, utilizamos a co-homologia das superfícies, com coeficientes locais, e também o método desenvolvido por Larmore para contar classes de homotopia de levantamento de funções.<br>The aim of this work is enumerate the plane bundles over some surfaces, for example the sphere and the g-torus. Among other tools we used cohomology of the surfaces with local coefficients and also the method developed by Larmore to count homotopy classes o

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Cotrim, Fabiana Santos. "Homotopias finitamente fixadas e pares de homotopias finitamente coincidentes." Universidade Federal de São Carlos, 2011. https://repositorio.ufscar.br/handle/ufscar/5876.

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Made available in DSpace on 2016-06-02T20:28:26Z (GMT). No. of bitstreams: 1 3729.pdf: 608631 bytes, checksum: 9ccfdd58a15118a67f48b346502a277e (MD5) Previous issue date: 2011-03-02<br>Financiadora de Estudos e Projetos<br>In the area of the theory of fixed points and coincidences of Nielsen, this study aims to develop techniques to minimize the set of fixed points in homotopies and the set of coincidences in pairs of homotopies. The techniques are based on Hopf construction for selfmaps of polyhedrons and on the results presented by Helga Schirmer in context of _x-finite homotopies. For pai

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Nguyen, Thi Kim Ngan. "Modules de cycles et classes non ramifiées sur un espace classifiant." Paris 7, 2010. http://www.theses.fr/2010PA077083.

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Cette thèse donne une nouvelle expression de la cohomologie non ramifiée H^*_nr(k(W)^G,Q/Z) en termes des groupes d'éléments partiellement non ramifiés sur un espace classifiant A^0(BH,H^*_et(Q/Z)) (H\subset G), où G est un groupe fini. Plus généralement, on utilise les modules de cycles de Rost et la cohomologie motivique de Voevodsky. Comme applications, on donne un résultat dual exprimant CH_0 du compactifié de BG en termes de l'homologie de Suslin en degré 0 H^S_0(BH,Z) (H\subset G), et on retrouve et généralise des formules dues à Bogomolov et Peyre pour la cohomologie non ramifiée en deg

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Aounil, Ismail. "Classes caractéristiques d'une opération en homologie cyclique." Toulouse 3, 1992. http://www.theses.fr/1992TOU30020.

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On associe a une opération d'une algèbre différentielle graduée sur un module cyclique des classes caractéristiques qu'on obtient en construisant une extension dans les algèbres différentielles graduées prolongeant en degré zéro la cohomologie cyclique bivariante de Jones-Kassel. Ceci nous permet de calculer la première différentielle de la suite spectrale de Tsygan-Nistor qui converge vers la partie homogène de l'homologie cyclique d'un produit croisé.

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Robinson, Daniel Mark. "The homotopy exponent problem for certain classes of polyhedral products." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/the-homotopy-exponent-problem-for-certain-classes-of-polyhedral-products(a20ca2ac-540b-41e9-8af7-1f76d8f5ed84).html.

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Given a sequence of n topological pairs (X_i,A_i) for i=1,...,n, and a simplicial complex K, on n vertices, there is a topological space (X,A)^K by a construction of Buchstaber and Panov. Such spaces are called polyhedral products and they generalize the central notion of the moment-angle complex in toric topology. We study certain classes of polyhedral products from a homotopy theoretic point of view. The boundary of the 2-dimensional n-sided polygon, where n is greater than or equal to 3, may be viewed as a 1-dimensional simplicial complex with n vertices and n faces which we call the n-gon.

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Rivière, Alain. "Classification des points d'un ouvert d'un espace euclidien relativement à la distance au bord : étude topologique et quantitative des classes obtenues." Paris 11, 1987. http://www.theses.fr/1987PA112365.

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On étudie dans cette thèse l'ensemble N des points d'un ouvert Ω d'un espace euclidien qui ne se trouvent dans l'intérieur d'aucun segment joignant un point de Ω à l'une de ses projections sur le complémentaire Ӕ \Ω de Ω. Par exemple les points de Ω qui admettent plusieurs projections sur Ӕ\ Ω sont dans N; leur ensemble M est aussi le lieu des points de Ω de non différentiabilité de la fonction distance au bord de Ω. Nous étudions la rareté au sens de Baire, la négligeabilité, la dimension de Hausdorff de M et de N qui peuvent être denses dans Ω. Nous étudions les propriétés de connexité de M

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Núñez, Rodríguez Irene Edith. "Isomorfismo entre los grupos de homotopía de los delta grupos de clases de difeomorfismos y de trenzas sobre superficies." Bachelor's thesis, Universidad Nacional Mayor de San Marcos, 2012. https://hdl.handle.net/20.500.12672/10229.

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Publicación a texto completo no autorizada por el autor<br>Describe la estructura de conjuntos, homología de conjuntos y la - estructura de grupos cruzados para dar cabida a la construcción de estructuras en el grupos de trenzas y el grupo de clases de difeomorfismos con la finalidad de discutir la relación que éstas tienen y así establecer un isomorfismo entre ellas.<br>Tesis

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Cuerington, Andre M. "The shortest path problem in the plane with obstacles : bounds on path lengths and shortest paths within homotopy classes." Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/28532.

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Jenkins, Kevin Dean. "The shortest path problem in the plane with obstacles : a graph modeling approach to producing finite search lists of homotopy classes." Thesis, Monterey, California. Naval Postgraduate School, 1991. http://hdl.handle.net/10945/26761.

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The problem of finding the shortest path between two points in a plane containing obstacles is considered. The set of such paths is uncountably infinite, making an exhaustive search impossible. This difficulty is overcome by reducing the size of the search space. The search is first restricted to a countably infinite set by focusing attention on the set of homotopy classes. By applying simple optimality principles, a finite list of such classes is obtained whose union contains the shortest path. This process of simplification is accomplished by modeling the topology of the region with a graph.

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Books on the topic "Classes de homotopia"

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Cuerington, Andrè M. The shortest path problem in the plane with obstacles: Bounds on path lengths and shortest paths within homotopy classes. Naval Postgraduate School, 1991.

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Jenkins, Kevin Dean. The shortest path problem in the plane with obstacles: A graph modeling approach to producing finite search lists of homotopy classes. Naval Postgraduate School, 1991.

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Stanford Symposium on Algebraic Topology: Applications and New Directions (2012 : Stanford, Calif.), ed. Algebraic topology: Applications and new directions : Stanford Symposium on Algebraic Topology: Applications and New Directions, July 23--27, 2012, Stanford University, Stanford, CA. American Mathematical Society, 2014.

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1932-, Bass Hyman, and Lam, T. Y. (Tsit-Yuen), 1942-, eds. Algebra. American Mathematical Society, 2010.

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Farb, Benson, and Dan Margalit. Mapping Class Group Basics. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0003.

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This chapter explains the basics of the mapping class group of a surface. It first provides the definition and examples before computing the mapping class group in essentially all of the cases where it can be computed directly. This includes the case of the disk, the annulus, the torus, and the pair of pants. An important method, the Alexander method, emerges as a tool for such computations and is used to prove whether a homeomorphism is or is not homotopically trivial, and whether two homeomorphisms are homotopic or not. One of the computations performed using the Alexander method is a classi

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Farb, Benson, and Dan Margalit. Curves, Surfaces, and Hyperbolic Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0002.

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This chapter explains the basics of working with simple closed curves, focusing on the case of the closed surface Sɡ of genus g. When g is greater than or equal to 2, hyperbolic geometry enters as a useful tool since each homotopy class of simple closed curves has a unique geodesic representative. The chapter begins by recalling some basic results about surfaces and hyperbolic geometry, with particular emphasis on the boundary of the hyperbolic plane and hyperbolic surfaces. It then considers simple closed curves in a surface S, along with geodesics and intersection numbers. It also discusses

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McDuff, Dusa, and Dietmar Salamon. Linear symplectic geometry. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0003.

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The second chapter introduces the basic concepts of symplectic topology in the linear algebra setting, such as symplectic vector spaces, the linear symplectic group, Lagrangian subspaces, and the Maslov index. In the section on linear complex structures particular emphasis is placed on the homotopy equivalence between the space of symplectic forms and the space of linear complex structures. The chapter includes sections on symplectic vector bundles and the first Chern class.

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Book chapters on the topic "Classes de homotopia"

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Switzer, Robert M. "Characteristic Classes." In Algebraic Topology — Homotopy and Homology. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-61923-6_17.

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Casacuberta, Carles, and Jiří Rosický. "Combinatorial Homotopy Categories." In Bousfield Classes and Ohkawa's Theorem. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1588-0_4.

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Penner, Robert. "Exact Sequences of Homotopy Classes." In Lecture Notes in Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-43996-5_21.

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Roitberg, Joseph. "Computing homotopy classes of phantom maps." In CRM Proceedings and Lecture Notes. American Mathematical Society, 1994. http://dx.doi.org/10.1090/crmp/006/08.

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Siegel, Jerrold. "Extrema associated with homotopy classes of maps." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0075229.

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Faticoni, Theodore G. "Modules Over Endomorphism Rings as Homotopy Classes." In Abelian Groups and Modules. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0443-2_13.

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Zhou, Xueguang. "Higher cohomology operations that detect homotopy classes." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085245.

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Hayat-Legrand, Claude. "Classes homotopiques associees a une G-operation." In Algebraic Topology Homotopy and Group Cohomology. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0087507.

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Kato, Ryo, Hiroki Okajima, and Katsumi Shimomura. "Notes on an Algebraic Stable Homotopy Category." In Bousfield Classes and Ohkawa's Theorem. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1588-0_5.

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Binz, Ernst, and Sonja Pods. "Isomorphism classes, Chern classes and homotopy classes of singularity free vector fields in 3-space." In The Geometry of Heisenberg Groups. American Mathematical Society, 2008. http://dx.doi.org/10.1090/surv/151/04.

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Conference papers on the topic "Classes de homotopia"

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Caro, Stephane, Philippe Wenger, and Fouad Bennis. "Robustness Study of Generic and Non-Generic 3R Positioning Manipulators." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84903.

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This paper presents a robustness study of 3R manipulators and aims at answering the following question: are generic manipulators more robust than non-generic manipulators? We exploit several properties specific to 3R manipulators such as singularities, cuspidality, homotopy classes, and path feasibility, in order to find some correlations between genericity and robustness concepts. For instance, we show that generic manipulators, close to non-generic ones in the space of geometric parameters, are not robust with respect to their homotopy class and to the feasibility of paths. Moreover, we noti

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Kawazumi, Nariya. "Twisted Morita–Mumford classes on braid groups." In Groups, homotopy and configuration spaces, in honour of Fred Cohen's 60th birthday. Mathematical Sciences Publishers, 2008. http://dx.doi.org/10.2140/gtm.2008.13.293.

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"A Bug-based Path Planner Guided with Homotopy Classes." In 9th International Conference on Informatics in Control, Automation and Robotics. SciTePress - Science and and Technology Publications, 2012. http://dx.doi.org/10.5220/0004041201230131.

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Hernandez, Emili, Marc Carreras, Javier Antich, Pere Ridao, and Alberto Ortiz. "A topologically guided path planner for an AUV using homotopy classes." In 2011 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2011. http://dx.doi.org/10.1109/icra.2011.5980108.

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Kolur, Keshav, Sahit Chintalapudi, Byron Boots, and Mustafa Mukadam. "Online Motion Planning Over Multiple Homotopy Classes with Gaussian Process Inference." In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2019. http://dx.doi.org/10.1109/iros40897.2019.8967598.

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Kim, Donghyuk, Mincheul Kang, and Sung-Eui Yoon. "Volumetric Tree*: Adaptive Sparse Graph for Effective Exploration of Homotopy Classes." In 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2019. http://dx.doi.org/10.1109/iros40897.2019.8967728.

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Wei Zeng, Miao Jin, Feng Luo, and Xianfeng David Gu. "Canonical homotopy class representative using hyperbolic structure." In 2009 IEEE International Conference on Shape Modeling and Applications (SMI). IEEE, 2009. http://dx.doi.org/10.1109/smi.2009.5170145.

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Hernandez, Emili, Marc Carreras, Enric Galceran, and Pere Ridao. "Path planning with homotopy class constraints on bathymetric maps." In OCEANS 2011 - SPAIN. IEEE, 2011. http://dx.doi.org/10.1109/oceans-spain.2011.6003519.

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Tan, Jiawei, Jia Chen, and Qinghuai Liu. "Homotopy Method for a Class of Fixed-Point Problems." In 2010 Third International Joint Conference on Computational Science and Optimization. IEEE, 2010. http://dx.doi.org/10.1109/cso.2010.236.

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Bhattacharya, Subhrajit, Maxim Likhachev, and Vijay Kumar. "Identification and Representation of Homotopy Classes of Trajectories for Search-based Path Planning in 3D." In Robotics: Science and Systems 2011. Robotics: Science and Systems Foundation, 2011. http://dx.doi.org/10.15607/rss.2011.vii.002.

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