Realizability of the group of rational self-homotopy equivalences

Details Realizability of the group of rational self-homotopy equivalences Realizability of the group of rational self-homotopy equivalences

2010-10-07

arxiv.org/abs/1010.1441v1

Mathematics

Algebraic Topology

Scientific paper

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational CW-complex $X_{n}$ such that $\mathcal{E}(X_{n})\cong \underset{2^{n+1}\mathrm{. times}}{\underbrace{\Bbb Z_{2}\oplus... \Bbb \oplus \Bbb Z_{2}}}$.

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