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arXiv · 2110.13888

Every group is the group of self homotopy equivalences of finite dimensional CW-complex

Mahmoud Benkhalifa
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Abstract

We prove that any group $G$ occurs as $\E(X)$, where $X$ is CW-complex of finite dimension and $\E(X)$ denotes its group of self-homotopy equivalence. Thus, we generalize a well know-theorem due to Costoya and Viruel \cite{CV} asserting that any finite group occurs as $\E(X)$, where $X$ is rational elliptic space.

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Mahmoud Benkhalifa. 2021-10-26. Every group is the group of self homotopy equivalences of finite dimensional CW-complex. https://arxiv.org/abs/2110.13888

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