Monoids of self-maps of topological spherical space forms

TL;DR

This paper demonstrates that the monoid of homotopy classes of self-maps of topological spherical space forms depends solely on the acting group and sphere dimension, regardless of the specific group action.

Contribution

It establishes that the monoid structure is invariant under different free actions of the same group on spheres, depending only on the group and dimension.

Findings

Monoid of self-maps determined by group and dimension

Homotopy types depend on group actions, but monoids do not

Invariant monoid structure across different actions

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.