THE GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

Title & Authors
THE GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES
Lee, Kee-Young;

Abstract
In this paper, we extend the concept of the group $\small{{\varepsilon}(X)}$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group $\small{{\varepsilon}(X,\;A)}$ of pair homotopy equivalences from a CW-pair (X, A) to itself which is the special case of the extended concept. For a CW-pair (X, A), we find an exact sequence $\small{1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)}$ where G is a subgroup of $\small{{\varepsilon}(X,\;A)}$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $\small{1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1}$ provided the two sets $\small{[X{\wedge}Y,\;X{\times}Y]}$ and [X, Y] are trivial.
Keywords
self homotopy equivalence;self pair homotopy equivalence;
Language
English
Cited by
1.
Certain numbers on the groups of self-homotopy equivalences, Topology and its Applications, 2015, 181, 104
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