Homotopy equivalences of localized aspherical complexes

Details Homotopy equivalences of localized aspherical complexes Homotopy equivalences of localized aspherical complexes

2007-03-26

arxiv.org/abs/math/0703765v1

Mathematics

Algebraic Topology

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

Scientific paper

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.

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