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THE GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES

Lee, Kee-Young   (Department of Information and Mathematics Korea UniversityUU0000159  );
  • 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.


  • 주제어

    self homotopy equivalence .   self pair homotopy equivalence.  

  • 참고문헌 (12)

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 저자의 다른 논문

  • Lee, Kee-Young (8)

    1. 2004 "POSTNIKOV SECTIONS AND GROUPS OF SELF PAIR HOMOTOPY EQUIVALENCES" Bulletin of the Korean Mathematical Society = 대한수학회보 41 (3): 393~401    
    2. 2005 "COHOMOLOGY AND GENERALIZED GOTTLIEB GROUPS" 충청수학회지 = Journal of the Chungcheong Mathematical Society 18 (1): 23~31    
    3. 2006 "COHOMOLOGY AND TRIVIAL GOTTLIEB GROUPS" Communications of the Korean Mathematical Society = 대한수학회논문집 21 (1): 185~191    
    4. 2008 "CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS" Bulletin of the Korean Mathematical Society = 대한수학회보 45 (1): 119~131    
    5. 2010 "GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS" Bulletin of the Korean Mathematical Society = 대한수학회보 47 (6): 1311~1327    
    6. 2016 "SOME COHOMOTOPY GROUPS OF SUSPENDED QUATERNIONIC PROJECTIVE PLANES" Bulletin of the Korean Mathematical Society = 대한수학회보 53 (5): 1567~1583    
    7. 2017 "SELF-HOMOTOPY EQUIVALENCES RELATED TO COHOMOTOPY GROUPS" Journal of the Korean Mathematical Society = 대한수학회지 54 (2): 399~415    
    8. 2017 "FACTORIZATION OF CERTAIN SELF-MAPS OF PRODUCT SPACES" Journal of the Korean Mathematical Society = 대한수학회지 54 (4): 1231~1242    

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