Finite groups as homotopy self-equivalences of finite spaces

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Finite groups as homotopy self-equivalences of finite spaces

Juan Felipe Celis-Rojas – GJM, Volume 9, Issue 2 (2024), 15-21.

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.

Categories: 2024, Issue2

Milestones:

Received: November 5, 2024
Accepted: December 4, 2024
Revised: December 12, 2024
Published: December 30, 2024.

Authors:

Juan Felipe Celis-Rojas
Institute of Mathematics
EPFL SB MATH MA A2 383 (Bâtiment MA), Station 8
CH-1015 Lausanne, Switzerland

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