대한수학회지 (Journal of the Korean Mathematical Society)

  • 제54권5호
  • /
  • Pages.1623-1639
  • /
  • 2017
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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THE GENERALIZED COGOTTLIEB GROUPS, RELATED ACTIONS AND EXACT SEQUENCES

  • Choi, Ho-Won (Department of Mathematics Korea University) ;
  • Kim, Jae-Ryong (Department of Mathematics Kookmin University) ;
  • Oda, Nobuyuki (Department of Applied Mathematics Faculty of Science Fukuoka University)
  • 투고 : 2016.09.13
  • 심사 : 2016.12.26
  • 발행 : 2017.09.01
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초록

The generalized coGottlieb sets are not known to be groups in general. We study some conditions which make them groups. Moreover, there are actions on the generalized coGottlieb sets which are different from known actions up to now. We give related exact sequence of the generalized coGottlieb sets. Using them, we obtain certain results related to the maps which preserve generalized coGottlieb sets.

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과제정보

연구 과제 주관 기관 : Kookmin University, JSPS KAKENHI

참고문헌

  1. M. Arkowitz, Introduction to Homotopy Theory, Universitext, Springer, New York, 2011.
  2. M. Arkowitz, G. Lupton, and A. Murillo, Subgroups of the group of self-homotopy equivalences, Groups of homotopy self-equivalences and related topics (Gargnano, 1999), 21-32, Contemp. Math., 274, Amer. Math. Soc., Providence, RI, 2001.
  3. D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. https://doi.org/10.2307/2373349
  4. B. Gray, Homotopy Theory, Academic Press, 1975.
  5. H. B. Haslam, G-spaces and H-spaces, Thesis, University of California at Irvine, 1969.
  6. H. B. Haslam, G-spaces mod F and H-spaces mod F, Duke Math. J. 38 (1971), 671-679. https://doi.org/10.1215/S0012-7094-71-03882-8
  7. J.-R. Kim and N. Oda, Cocyclic element preserving pair maps and fibrations, Topology Appl. 191 (2015), 82-96. https://doi.org/10.1016/j.topol.2015.05.052
  8. K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), no. 1, 63-71. https://doi.org/10.4153/CMB-1987-009-1
  9. C. R. F. Maunder, Algebraic Topology, Cambridge University Press, 1980.
  10. N. Oda, The homotopy set of the axes of pairings, Canad. J. Math. 42 (1990), no. 5, 856-868. https://doi.org/10.4153/CJM-1990-044-3
  11. N. Oda, Pairings and copairings in the category of topological spaces, Publ. Res. Inst. Math. Sci. 28 (1992), no. 1, 83-97. https://doi.org/10.2977/prims/1195168857
  12. K. Varadarajan, Generalised Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
  13. G. W. Whitehead, Elements of homotopy theory, Graduate texts in Mathematics 61, Springer-Verlag, New York Heidelberg Berlin, 1978.
  14. Y. S. Yoon, The generalized dual Gottlieb sets, Topology Appl. 109 (2001), no. 2, 173-181. https://doi.org/10.1016/S0166-8641(99)00150-9