Certain self-homotopy equivalences on wedge products of Moore spaces (Q482089)

Let \(X\) be a based \(1\)-connected finite \(CW\) complex of dimension \(d\), and \({\mathcal E}_{\# }^{d+r}(X)\) the group of homotopy classes of based self-homotopy equivalences that induce the identity automorphism of on \(\pi _s(X)\) for all \(s\leq d+r\). For Moore spaces \(M_1 = M({\mathbb Z}_q , n+1) = S^{n+1} \cup _q e^{n+2}\) and \(M_2 = M({\mathbb Z}_p , n) = S^n \cup _p e^{n+1}\), the authors determine \({\mathcal E}_{\# }^{d+r}(M_1\vee M_2)\) where \(p,q \geq 2\) for \(n\geq 5\) and \(r=0,1\). Earlier results were given for \(X=M({\mathbb Z}_p , n)\) by M. Arkowitz and K. I. Maruyama, and for the case where \(p=q\) by M. H. Jeong. The proofs given proceed by the \(2\times 2\) matrix representation with components \([M_i ,M_j ]\) for \(i,j=1,2\).