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 | |
Publication status | Published - 1 Jan 2003 |