Some Properties of Aut_*(X) and the Subgroup Aut_Σ(X)

摘要

Let Aut*(X) denote the group of homotopy classes of self-homotopy equivalences of X, which induce identity automorphisms of homology group. We describe a decomposition of Aut*(X1∨…∨Xn) as a product of its simpler subgroups. We consider the subgroup AutΣ (X) of all self homotopy classes α of X such that Σα = 1ΣX : ΣX→ΣX, and also give some properties of AutΣ (X).