DOI QR코드

DOI QR Code

CERTAIN GENERALIZATIONS OF G-SEQUENCES AND THEIR EXACTNESS

  • Lee, Kee-Young (DEPARTMENT OF INFORMATION AND MATHEMATICS KOREA UNIVERSITY) ;
  • Woo, Moo-Ha (DEPARTMENT OF MATHEMATICS KOREA UNIVERSITY) ;
  • Zhao, Xuezhi (DEPARTMENT OF MATHEMATICS CAPITA NORMAL UNIVERSITY)
  • Published : 2008.02.29

Abstract

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.

Keywords

References

  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 https://doi.org/10.2307/2373695
  2. R. F. Brown, The Lefschetz Fixed Point Theorem, Scott, Foresman and Co., Glenview, Ill.-London 1971
  3. D. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856 https://doi.org/10.2307/2373248
  4. D. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756 https://doi.org/10.2307/2373349
  5. D. Gottlieb, Covering transformations and universal fibrations, Illinois J. Math. 13 (1969), 432-437
  6. B. Jiang, Estimation of the Nielsen numbers, Acta Math. Sinica 14 (1964), 304-312
  7. B. Jiang, Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, 14. American Mathematical Society, Providence, R.I., 1983
  8. T. H. Kiang, The Theory of Fixed Point Classes, Translated from the second Chinese edition. Springer-Verlag, Berlin; Science Press, Beijing, 1989
  9. K. Lee and M. Woo, The G-sequence and the $\omega$-homology of CW-pair, Topology Appl. 52 (1993), no. 3, 221-236 https://doi.org/10.1016/0166-8641(93)90104-L
  10. 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 https://doi.org/10.1016/j.jpaa.2006.05.018
  11. J. Pak and M. Woo, A remark on G-sequences, Math. Japon. 46 (1997), no. 3, 427-432
  12. 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
  13. M. Woo and J. Kim, Certain subgroups of homotopy groups, J. Korean Math. Soc. 21 (1984), no. 2, 109-120
  14. M. Woo and K. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160
  15. M. Woo and Y. Yoon, Certain subgroups of homotopy groups of a transformation group, J. Korean Math. Soc. 20 (1983), no. 2, 223-233
  16. X. Zhao, Realization of fixed point sets, Acta Math. Sinica (N.S.) 12 (1996), no. 1, 71-76 https://doi.org/10.1007/BF02109393

Cited by

  1. GOTTLIEB SUBSETS WITH RESPECT TO A MORPHISM IN THE CATEGORY OF PAIRS vol.47, pp.6, 2010, https://doi.org/10.4134/BKMS.2010.47.6.1311