POSTNIKOV SECTIONS AND GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

Title & Authors
POSTNIKOV SECTIONS AND GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES
Lee, Kee-Young;

Abstract
In this paper, we apply the concept of the group \ulcorner(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$\small{\sub}$n/ of a CW-complex X, the group \ulcorner(X$\small{\sub}$n/, A) of self pair homotopy equivalences on the pair (X$\small{\sub}$n/, X) is isomorphic to the group \ulcorner(X) of self homotopy equivalences on X. As a corollary, we have, \ulcorner(K($\small{\pi}$, n), M($\small{\pi}$, n)) ≡ \ulcorner(M($\small{\pi}$, n)) for each n$\small{\pi}$1, where K($\small{\pi}$,n) is an Eilenberg-Mclane space and M($\small{\pi}$,n) is a Moore space.
Keywords
self homotopy equivalence;self pair homotopy equivalence;Postnikov section;
Language
English
Cited by
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