Contractible simplicial objects

Michael Barr; John F. Kennison; Robert M. Raphael

Displaying similar documents to “Contractible simplicial objects”

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 $f$ - and $h$ -triangle of the barycentric subdivision of a simplicial complex

Sarfraz Ahmad (2013)

Czechoslovak Mathematical Journal

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For a simplicial complex $Δ$ we study the behavior of its $f$ - and $h$ -triangle under the action of barycentric subdivision. In particular we describe the $f$ - and $h$ -triangle of its barycentric subdivision $sd (Δ)$ . The same has been done for $f$ - and $h$ -vector of $sd (Δ)$ by F. Brenti, V. Welker (2008). As a consequence we show that if the entries of the $h$ -triangle of $Δ$ are nonnegative, then the entries of the $h$ -triangle of $sd (Δ)$ are also nonnegative. We conclude with a few properties of the $h$ -triangle of $sd (Δ)$ . ...

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.

A general theory of polyhedral sets and the corresponding T-complexes

David W. Jones

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PrefaceThis paper is essentially David Jones' 1984 University of Wales Ph. D. Thesis, "Poly-T-complexes". It is published concurrently with Asley, 1988.The main aim is to find a setting for the most general kinds of geometrically defined compositions. Thus it comes under the slogan: "Find an algebraic inverse to subdivision". In the background is the Generalised Van Kampen Theorem, whose proof uses in an essential way general compositions of cubes. An even older background is the idea...

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...

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).

On the homotopy transfer of $A_{\infty}$ structures

Jakub Kopřiva (2017)

Archivum Mathematicum

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The present article is devoted to the study of transfers for $A_{\infty}$ structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.

Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska (2001)

Fundamenta Mathematicae

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Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space $(B_{p} (G)) / G$ of the classifying space of the category associated to the G-poset $_{p} (G)$ of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor $X^{E ₙ} / (N E ₀ \cap . . . \cap N E ₙ)$ defined over the poset $(s d_{p} (G)) / G$ , where sd is the barycentric subdivision....

Interplay between strongly universal spaces and pairs

Taras Banakh, Robert Cauty

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Given a pair (M,X) of spaces we investigate the connections between the (strong) universality of (M,X) and that of the space X. We apply this to prove Enlarging, Deleting, and Strong Negligibility Theorems for strongly universal and absorbing spaces. Given an absorbing space Ω we also study the question of topological uniqueness of the pair (M,X), where $M = {[0, 1]}^{ω}$ or $M = {(0, 1)}^{ω}$ and X is a copy of Ω in M having a locally homotopy negligible complement in M.

Algebraic tori as Nisnevich sheaves with transfers

Bruno Kahn (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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We relate $R$ -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.

From binary cube triangulations to acute binary simplices

Brandts, Jan, van den Hooff, Jelle, Kuiper, Carlo, Steenkamp, Rik

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Cottle’s proof that the minimal number of $0 / 1$ -simplices needed to triangulate the unit $4$ -cube equals $16$ uses a modest amount of computer generated results. In this paper we remove the need for computer aid, using some lemmas that may be useful also in a broader context. One of the $0 / 1$ -simplices involved, the so-called antipodal simplex, has acute dihedral angles. We continue with the study of such acute binary simplices and point out their possible relation to the Hadamard determinant problem. ...

An application of principal bundles to coloring of graphs and hypergraphs

Milgram, James R., Zvengrowski, Peter

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An interesting connection between the chromatic number of a graph $G$ and the connectivity of an associated simplicial complex $N (G)$ , its “neighborhood complex”, was found by Lovász in 1978 (cf. [J. Comb. Theory, Ser. A 25, 319-324 (1978; Zbl 0418.05028)]). In 1986 a generalization to the chromatic number of a $k$ -uniform hypergraph $H$ , for $k$ an odd prime, using an associated simplicial complex $C (H)$ , was found ([, and , Trans. Am. Math. Soc. 298, 359-370 (1986; Zbl 0605.05033)], Prop. 2.1). It...