Homotopy equivalences of p-completed classifying spaces of finite groups
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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 ℒpc(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 ℒpc(G) and ℒpc(G’) are equivalent. Furthermore, the topological monoid Aut(BGp∧) of self equivalences is determined by the self equivalences of the associated category ℒpc(G).
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