Homotopy equivalences of localized aspherical complexes

2007/03/26 by Garvín, A., Murillo, A., Remedios, J. +1
#55P10 #55P20 #55P60 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0703765

Abstract

By studying the group of self homotopy equivalences of the localization (at a prime p and/or zero) of some aspherical complexes, we show that, contrary to the case when the considered space is a nilpotent complex, E_#^m (X_p) is in general different from E_#^m (X)_p. That is the case even when X=K(G,1) is a finite complex and/or G satisfies extra finiteness or nilpotency conditions, for instance, when G is finite or virtually nilpotent.

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