Equivariant self-homotopy equivalences of product spaces

TL;DR

This paper investigates the structure of G-equivariant self-homotopy equivalences of product G-spaces, providing new decompositions and representations under equivariant reducibility assumptions.

Contribution

It introduces a novel $LU$ type decomposition and describes the group structure of equivariant self-homotopy equivalences for product G-spaces.

Findings

Representation of the group as a product of n-subgroups

Description of each factor via split short exact sequences

Introduction of $LU$ type decomposition as a product of two subgroups

Abstract

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n-spaces, we represent it as product of n-subgroups under the assumption of equivariant reducibility. Further we describe each factor as a split short exact sequence. Also, we obtain an another kind of factorisation, called $LU$ type decomposition, as product of two subgroups.