Finite groups as homotopy self-equivalences of finite spaces

Juan Felipe Celis-Rojas

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arXiv · 2411.01005

Finite groups as homotopy self-equivalences of finite spaces

Juan Felipe Celis-Rojas

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Abstract

We study the realization problem of finite groups as the group of homotopy classes of self-homotopy equivalences of finite spaces. Let $G$ be a finite group. Using an infinite family of pairwise non weakly homotopic asymmetric spaces we present a new construction of a finite space whose group of homotopy classes of self-homotopy equivalences is isomorphic to $G$.

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Juan Felipe Celis-Rojas. 2024-11-01. Finite groups as homotopy self-equivalences of finite spaces. https://arxiv.org/abs/2411.01005

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