대한수학회지 (Journal of the Korean Mathematical Society)

  • 제43권3호
  • /
  • Pages.491-506
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  • 2006
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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THE GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

  • Lee, Kee-Young (Department of Information and Mathematics Korea University)
  • 발행 : 2006.05.01
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초록

In this paper, we extend the concept of the group ${\varepsilon}(X)$ of self homotopy equivalences of a space X to that of an object in the category of pairs. Mainly, we study the group ${\varepsilon}(X,\;A)$ 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 $1\;{\to}\;G\;{\to}\;{\varepsilon}(X,\;A)\;{to}\;{\varepsilon}(A)$ where G is a subgroup of ${\varepsilon}(X,\;A)$. Especially, for CW homotopy associative and inversive H-spaces X and Y, we obtain a split short exact sequence $1\;{\to}\;{\varepsilon}(X)\;{\to}\;{\varepsilon}(X{\times}Y,Y)\;{\to}\;{\varepsilon}(Y)\;{\to}\;1$ provided the two sets $[X{\wedge}Y,\;X{\times}Y]$ and [X, Y] are trivial.

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참고문헌

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피인용 문헌

  1. Certain maps preserving self-homotopy equivalences vol.12, pp.3, 2017, https://doi.org/10.1007/s40062-016-0144-0
  2. Certain numbers on the groups of self-homotopy equivalences vol.181, 2015, https://doi.org/10.1016/j.topol.2014.12.004