Postnikov sections and groups of self pair homotopy equivalences
Bull. Korean Math. Soc. 2004 Vol. 41, No. 3, 393-401
Published online September 1, 2004
Kee Young Lee
Korea University
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 related to the group of self pair homotopy equivalences, we obtain the following result: for any Postnikov section $X_n $ of a CW-complex $X$, the group $\mathcal{E}(X_n , X)$ of self pair homotopy equivalences on the pair $(X_n , X)$ is isomorphic to the group $ \mathcal{E} (X)$ of self homotopy equivalences on $X$. As a corollary, we have, $\mathcal{E}(K(\pi,n),M(\pi,n))\equiv\mathcal{E}(M(\pi,n))$ for each $n \geq 1$, where $K(\pi,n)$ is an Eilenberg-Mclane space and $M(\pi,n)$ is a Moore space.
Keywords : self homotopy equivalence, self pair homotopy equivalence, Postnikov section
MSC numbers : Primary 55P10; Secondary 55P30, 55P20
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