TY - JOUR
T1 - Homotopy equivalences of p-completed classifying spaces of finite groups
AU - Broto, Carles
AU - Levi, Ran
AU - Oliver, Bob
PY - 2003/1/1
Y1 - 2003/1/1
N2 - 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).
AB - 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).
U2 - https://doi.org/10.1007/s00222-002-0264-5
DO - https://doi.org/10.1007/s00222-002-0264-5
M3 - Article
VL - 151
SP - 611
EP - 664
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
ER -