Embedding proper homotopy types

M. Cárdenas; T. Fernández; F. F. Lasheras; A. Quintero

Displaying similar documents to “Embedding proper homotopy types”

On the homotopy type of $Diff (M^{n})$ and connected problems

Dan Burghelea (1973)

Annales de l'institut Fourier

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This paper reports on some results concerning: a) The homotopy type of the group of diffeomorphisms $Diff (M^{n})$ of a differentiable compact manifold $M^{n}$ (with $C^{\infty}$ -topology). b) the result of the homotopy comparison of this space with the group of all homeomorphisms Homeo $M^{n}$ (with $C^{o}$ -topology). As a biproduct, one gets new facts about the homotopy groups of $Diff (D^{n}, \partial D^{n}), {Top}_{n}$ , ${Top}_{n} / O_{n}$ and about the number of connected components of the space of topological and combinatorial pseudoisotopies. ...

G-ANR's with homotopy trivial fixed point sets

Sergey A. Antonyan (2007)

Fundamenta Mathematicae

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Let G be a compact group and X a G-ANR. Then X is a G-AR iff the H-fixed point set $X^{H}$ is homotopy trivial for each closed subgroup H ⊂ G.

Some results on homotopy theory of modules

Zheng-Xu He (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Seguendo le idee presentate nei lavori [1] e [2] si studiano le proprietà dei gruppi di $i$ -omotopia per moduli ed omomorfismi di moduli.

Homotopy over $B$ and under $A$

K. A. Hardie, K. H. Kamps (1987)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

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We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $h o c o l i m_{_{d}} G / d (-) \to | W |$ which is a (non-equivariant) homotopy equivalence, hence $h o c o l i m_{_{d}} E G \times_{G} F_{d} \to E G \times_{G} | W |$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy...

On the homotopy invariance of configuration spaces.

Aouina, Mokhtar, Klein, John R. (2004)

Algebraic & Geometric Topology

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Cohomology $C_{\infty}$ -algebra and rational homotopy type

Tornike Kadeishvili (2009)

Banach Center Publications

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In the rational cohomology of a 1-connected space a structure of $C_{\infty}$ -algebra is constructed and it is shown that this object determines the rational homotopy type.

Minimal component numbers of fixed point sets

Xuezhi Zhao (2003)

Fundamenta Mathematicae

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Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant $N^{C} (f; X, A)$ , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of $N^{C} (f; X, A)$ are given, which are very similar to those of the relative Nielsen number N(f;X,A).

A decomposition of $E^{3}$ into straight arcs and singletons

S. Armentrout

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CONTENTS1. Introduction............................................................................................................................................. 52. Notation and. terminology................................................................................................................... 63. Description of G.................................................................................................................................... 64. Preliminaries to the...

Variations on a theme of homotopy

Timothy Porter (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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The aim of this article is to bring together various themes from fairly elementary homotopy theory and to examine them, in part, from a historical and philosophical viewpoint.

Linking and coincidence invariants

Ulrich Koschorke (2004)

Fundamenta Mathematicae

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Given a link map f into a manifold of the form Q = N × ℝ, when can it be deformed to an “unlinked” position (in some sense, e.g. where its components map to disjoint ℝ-levels)? Using the language of normal bordism theory as well as the path space approach of Hatcher and Quinn we define obstructions $ω ̃_{ε} (f)$ , ε = + or ε = -, which often answer this question completely and which, in addition, turn out to distinguish a great number of different link homotopy classes. In certain cases they even...

Contractible simplicial objects

Michael Barr, John F. Kennison, Robert M. Raphael (2019)

Commentationes Mathematicae Universitatis Carolinae

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We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by $- 1$ , which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy...

Open subsets of fibrations

J. F. McClendon (1983)

Compositio Mathematica

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Modulo $C$ homotopy

J. R. Dennett (1982)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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