Postnikov sections and groups

Abstract

In this paper, we apply the concept of the group mathcal{E}(X, A) of self pair homotopy equivalences of a CW-pair (X,A)to the Postnikov system. By using a short exact sequence relatedto the group of self pair homotopy equivalences, we obtain thefollowing result: for any Postnikov section X_n of a CW-complexX, the group mathcal{E}(X_n , X) of self pair homotopyequivalences on the pair (X_n , X) is isomorphic to the group mathcal{E} (X) of self homotopy equivalences on X. As acorollary, we have,mathcal{E}(K(pi,n),M(pi,n))equivmathcal{E}(M(pi,n)) foreach n geq 1, where K(pi,n) is an Eilenberg-Mclane space andM(pi,n) is a Moore space.