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Bulletin of the Korean Mathematical Society = 대한수학회보 v.45 no.1, 2008년, pp.119 - 131   피인용횟수: 1

CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS

Lee, Kee-Young   (DEPARTMENT OF INFORMATION AND MATHEMATICS KOREA UNIVERSITYUU0000159  ); Woo, Moo-Ha   (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITYUU0000159  ); Zhao, Xuezhi   (DEPARTMENT OF MATHEMATICS CAPITA NORMAL UNIVERSITY  );
  • 초록

    In this paper, we generalize the Gottlieb groups and the related G-sequence of those groups, and present some sufficient conditions to ensure the exactness or non-exactness of G-sequences at some terms. We also give some applications of the exactness or non-exactness of G-sequences. Especially, we show that the non-exactness of G-sequences implies the non-triviality of homotopy groups of some function spaces.


  • 주제어

    Gottlieb group .   G-sequence .   homotopy group.  

  • 참고문헌 (16)

    1. R. Brooks, Certain subgroups of the fundamental group and the number of roots of f(x) = a, Amer. J. Math. 95 (1973), 720-728 
    2. D. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856 
    3. D. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756 
    4. D. Gottlieb, Covering transformations and universal fibrations, Illinois J. Math. 13 (1969), 432-437 
    5. B. Jiang, Estimation of the Nielsen numbers, Acta Math. Sinica 14 (1964), 304-312 
    6. B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983 
    7. T. H. Kiang, The Theory of Fixed Point Classes, Translated from the second Chinese edition. Springer-Verlag, Berlin; Science Press, Beijing, 1989 
    8. K. Lee and M. Woo, The G-sequence and the $\omega$-homology of CW-pair, Topology Appl. 52 (1993), no. 3, 221-236 
    9. G. Lupton and S. Smith, Rationalized evaluation subgroups of a map. I. Sullivan models, derivations and G-sequences, J. Pure Appl. Algebra 209 (2007), no. 1, 159-171 
    10. J. Pak and M. Woo, A remark on G-sequences, Math. Japon. 46 (1997), no. 3, 427-432 
    11. J. Pan, X. Shen, and M. Woo, The G-sequence of a map and its exactness, J. Korean Math. Soc. 35 (1998), no. 2, 281-294 
    12. M. Woo and J. Kim, Certain subgroups of homotopy groups, J. Korean Math. Soc. 21 (1984), no. 2, 109-120 
    13. M. Woo and K. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160 
    14. X. Zhao, Realization of fixed point sets, Acta Math. Sinica (N.S.) 12 (1996), no. 1, 71-76 
    15. R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.-London 1971 
    16. M. Woo and Y. Yoon, Certain subgroups of homotopy groups of a transformation group, J. Korean Math. Soc. 20 (1983), no. 2, 223-233 
  • 이 논문을 인용한 문헌 (1)

    1. 2010. "" Bulletin of the Korean Mathematical Society = 대한수학회보, 47(6): 1311~1327     

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