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The groups of self pair homotopy equivalences

이기영
대한수학회 (The Korean Mathematical Society)|2006.05|대한수학회지 (Journal of the KMS)|제43권 제3호|pp. 491-506

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Abstract

In this paper, we extend the concept of the group mathcal{E}(X) of self homotopy equivalences of a space X to that of anobject in the category of pairs. Mainly, we study the groupmathcal{E}(X, A) of pair homotopy equivalences from a CW-pair(X,A) to itself which is the special case of the extendedconcept. For a CW-pair (X,A), we find an exact sequence1rightarrow G rightarrow mathcal{E}(X, A)rightarrowmathcal{E}(A) where G is a subgroup of mathcal{E}(X, A).Especially, for CW homotopy associative and inversive H-spacesX and Y, we obtain a split short exact sequence 1rightarrowmathcal{E}(X) rightarrow mathcal{E}(X times Y, Y)rightarrowmathcal{E}(Y)rightarrow 1 provided the two sets [XwedgeY,Xtimes Y] and [X, Y] are trivial.

참고문헌 (10)

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  2. "On finiteness of subgroups of self-homotopy equivalences", 181, pp.1~25 (1995)
  3. "Localization of a certain subgroup of self-homotopy equivalences", 136, pp.293~ (1989)
  4. "On the group of self-homotopy equivalences of H-spaces of lowrank", pp.247 307~ (1981), Kyushu Univ.Ser. A 35
  5. "The group of self-equivalence classes of CW complexes", 93(2), pp.275~ (1983)
  6. "Self-homotopy equivalences of the total spaces of a sperebundle over a sphere", 7(3), pp.365~ (1984)
  7. "On the group of self-equivalences of the productspheres", 5, pp.69~ (1975)
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  9. "Twisted self-homotopy equivalences", 34, pp.789~ (1970)
  10. "Self-homotopy equivalences of a space with two nonvanishinghomotopy groups", 79(1), pp.134~ (1980)

관련 논문AI추천

Gottlieb Groups and Subgroups of the Group of Self-Homotopy Equivalences김재룡, 우무하, Jianzhong Pan, Nobuyuki Oda대한수학회 · 대한수학회지2006 · 제43권 제5호Self-pair homotopy equivalences related to co-variant functors신혜선, 이기영, 최호원대한수학회 · 대한수학회지2024 · 제61권 제3호Self-homotopy equivalences of Moore spaces depending on cohomotopy groups오형석, 이기영, 최호원대한수학회 · 대한수학회지2019 · 제56권 제5호CERTAIN SUBGROUPS OF SELF-HOMOTOPY EQUIVALENCES OF THE WEDGE OF TWO MOORE SPACES정명화대한수학회 · 대한수학회논문집2010 · 제25권 제1호On factorizations of the subgroups of self-homotopy equivalencesHao Zhao, Yi-Yun Shi대한수학회 · 대한수학회지2008 · 제45권 제4호SELF-HOMOTOPY EQUIVALENCES RELATED TO COHOMOTOPY GROUPS오형석, 이기영, 최호원대한수학회 · 대한수학회지2017 · 제54권 제2호

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