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Realizability of the group of rational self-homotopy equivalences

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Mahmoud Benkhalifa

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 $\mathcal{E}(X_{n})\cong
\underset{2^{n+1}\mathrm{. times }}{\underbrace{\Bbb Z_{2}\oplus\cdots \Bbb \oplus \Bbb Z_{2}}}$.

Journal of Homotopy and Related Structures, Vol. 5(2010), No. 1, p. 361-372