Some results on homotopy theory of modules

Zheng-Xu He

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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

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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.

Embedding proper homotopy types

M. Cárdenas, T. Fernández, F. F. Lasheras, A. Quintero (2003)

Colloquium Mathematicae

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We show that the proper homotopy type of any properly c-connected locally finite n-dimensional CW-complex is represented by a closed polyhedron in $ℝ^{2 n - c}$ (Theorem I). The case n - c ≥ 3 is a special case of a general proper homotopy embedding theorem (Theorem II). For n - c ≤ 2 we need some basic properties of “proper” algebraic topology which are summarized in Appendices A and B. The results of this paper are the proper analogues of classical results by Stallings [17] and Wall [20] for finite...

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.

On weak $i$ -homotopy equivalences of modules

Zheng-Xu He (1984)

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

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Si definisce il gruppo di $i$ —omotopia di un singolo modulo e si introduce la nozione di equivalenza $i$ -omotopica debole. Sotto determinate condizioni per l'anello di base $\Lambda$ oppure per i moduli considerati, le equivalenze $i$ -omotopiche deboli coincidono con le equivalenze $i$ -omotopiche (forti).

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...

Homotopy over $B$ and under $A$

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

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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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).

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...

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...

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.

Suite spectrale du coniveau et $t$ -structure homotopique

Frédéric Déglise (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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Dans cette note, nous montrons que la suite spectrale du coniveau associée à un spectre motivique sur un corps parfait coïncide avec sa suite spectrale d’hypercohomologie pour la t-structure homotopique.

Some geometric perspectives in concurrency theory.

Goubault, Eric (2003)

Homology, Homotopy and Applications

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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.

Modulo $C$ homotopy

J. R. Dennett (1982)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Homotopy properties of the space of continuous paths. II - The general case with arbitrary boundary sets

Hu, Sze-Tsen (1952)

Portugaliae mathematica

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