Homotopy equivalences of p-completed classifying spaces of finite groups

Carles Broto; Ran Levi; Bob Oliver

doi:https://doi.org/10.1007/s00222-002-0264-5

Homotopy equivalences of p-completed classifying spaces of finite groups

Carles Broto, Ran Levi, Bob Oliver

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

47 Citations (Scopus)

Abstract

We study homotopy equivalences of p-completions of classifying spaces of finite groups. To each finite group G and each prime p, we associate a finite category lcp(G) with the following properties. Two p-completed classifying spaces BGp∧ and BG′p∧ have the same homotopy type if and only if the associated categories lcp(G) and =lcp(G') are equivalent. Furthermore, the topological monoid Aut(BGp∧) of self equivalences is determined by the self equivalences of the associated category lcp(G).

Original language	English
Pages (from-to)	611-664
Journal	Inventiones Mathematicae
Volume	151
DOIs	https://doi.org/10.1007/s00222-002-0264-5
Publication status	Published - 1 Jan 2003

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abstract = "We study homotopy equivalences of p-completions of classifying spaces of finite groups. To each finite group G and each prime p, we associate a finite category lcp(G) with the following properties. Two p-completed classifying spaces BGp∧ and BG′p∧ have the same homotopy type if and only if the associated categories lcp(G) and =lcp(G') are equivalent. Furthermore, the topological monoid Aut(BGp∧) of self equivalences is determined by the self equivalences of the associated category lcp(G).",

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