Homotopy equivalences of localized aspherical complexes

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, ${\mathcal{E}}_{\#}^m(X_p)$ is in general different from ${\mathcal{E}}_{\#}^m(X{)}_p$. 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.

6 pages, no figures. to appear in Math. Nach

References in corpus (1)

• Nilpotency of self homotopy equivalences with coefficients