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http://dx.doi.org/10.4134/BKMS.2004.41.3.393

POSTNIKOV SECTIONS AND GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

Lee, Kee-Young (Department of Information and Mathematics, Korea University)

Publication Information

Bulletin of the Korean Mathematical Society / v.41, no.3, 2004 , pp. 393-401 More about this Journal

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 $\sub$ n/ of a CW-complex X, the group \ulcorner(X $\sub$ n/, A) of self pair homotopy equivalences on the pair (X $\sub$ n/, X) is isomorphic to the group \ulcorner(X) of self homotopy equivalences on X. As a corollary, we have, \ulcorner(K( $\pi$ , n), M( $\pi$ , n)) ≡ \ulcorner(M( $\pi$ , n)) for each n $\pi$ 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;

Citations & Related Records

Reference

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