Homotopy equivalences of p-completed classifying spaces of finite groups

Carles Broto, Ran Levi, Bob Oliver

Research output: Contribution to journalArticleResearchpeer-review

48 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 languageEnglish
Pages (from-to)611-664
JournalInventiones Mathematicae
Volume151
DOIs
Publication statusPublished - 1 Jan 2003

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