Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Monoids of self-maps of topological spherical space forms

Pages: 141 – 149

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a8

Authors

Daisuke Kishimoto (Department of Mathematics, Kyoto University, Kyoto, Japan)

Nobuyuki Oda (Department of Applied Mathematics, Faculty of Science, Fukuoka University, Fukuoka, Japan)

Abstract

A topological spherical space form is the quotient of a sphere by a free action of a finite group. In general, their homotopy types depend on specific actions of a group. We show that the monoid of homotopy classes of self-maps of a topological spherical space form is determined by the acting group and the dimension of the sphere, not depending on a specific action.

Keywords

monoid of self-maps, topological spherical space form, equivariant Hopf theorem

2010 Mathematics Subject Classification

55Q05

Received 20 April 2020

Accepted 11 October 2020

Published 3 November 2021