The order of the group of self-homotopy equivalence of wedge spaces

TL;DR

This paper investigates the structure and order of the group of self-homotopy equivalences of wedge spaces, providing a decomposition under reducibility and a formula for the suspended case, generalizing previous results.

Contribution

It introduces a decomposition of the automorphism group for wedge spaces with multiple factors and extends known results to more general cases.

Findings

Decomposition of automorphism groups under reducibility

Formula for automorphisms of suspended wedge spaces

Generalization of previous results for multiple wedge factors

Abstract

In this paper $Aut(\Sigma X\vee \Sigma Y)^\#$ the order of the group of self-homotopy equivalence of wedge spaces is studied. Under the condition of reducibility, we decompose $ Aut(\bigvee\limits_{t=1}^{k}X_{t})$ to the product of subgroups which generalizes the known results for $k=2$. Then we also give the formula for $ Aut(\bigvee\limits_{t=1}^{k}\Sigma X_{t})^{\#}$.