SELF-HOMOTOPY EQUIVALENCES OF MOORE SPACES DEPENDING ON COHOMOTOPY GROUPS

Abstract

Given a topological space X and a non-negative integer k, epsilon(#)(k)(X) is the set of all self-homotopy equivalences of X that do not change maps from X to an t-sphere S-t homotopically by the composition for all t >= k. This set is a subgroup of the self-homotopy equivalence group epsilon(X). We find certain homotopic tools for computations of epsilon(#)(k)(X). Using these results, we determine epsilon(#)(k) (M(G,n)) for k >= n, where M(G, n) is a Moore space type of (G, n) for a finitely generated abelian group G.