Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

GENERALIZED DUAL GOTTLIEB SETS AND COCATEGORIES

  • Yoon, Yeon Soo (Department of Mathematics Education Hannam University) ;
  • Kim, Hak Do (Department of Mathematics Education Hannam University)
  • Published : 2012.02.15
⟨ Previous Next ⟩

Abstract

In this paper, we introduce the concepts of $DC^{p}_{k}$-spaces for maps which are the dual concepts of $C^{f}_{k}$-spaces for maps, and characterize $DC^{p}_{k}$-spaces for maps using the dual Gottlieb sets for maps and the LS cocategories.

Keywords

References

  1. J. Aguade, Decomposable free loop spaces, Can. J. Math. 39 (1987), 938-955. https://doi.org/10.4153/CJM-1987-047-9
  2. T. Ganea, Lusternik-Schnirelmann category and cocategory, Proc. London Math. Soc. (3)10 (1960), 623-639.
  3. T. Ganea, A generalization of the homology and homotopy suspension, Comment. Math. Helv. 39 (1965), 295-322.
  4. N. Iwase, Ganea's conjecture on Lusternik-Schnirelmann category, Bull. Lon. Math. Soc. 30 (1998), 623-634. https://doi.org/10.1112/S0024609398004548
  5. N. Iwase, M. Mimura, N. Oda and Y. S. Yoon, The Milnor-Stasheff filtration on spaces and generalized cyclic maps, to appear in Canad. Math. Bull.,
  6. I. M. James, On category in the sense of Lusternik-Schnirelmann, Topology 17 (1978), 331-348. https://doi.org/10.1016/0040-9383(78)90002-2
  7. K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), 63-71. https://doi.org/10.4153/CMB-1987-009-1
  8. J. Milnor, Construction of universal bundles, I, II, Ann. Math. 63 (1956), 272-284, 430-436. https://doi.org/10.2307/1969609
  9. N. Oda, The homotopy of the axes of pairings, Canad. J. Math. 17 (1990), 856-868.
  10. J. D. Stasheff, Homotopy associativity of H-spaces I, II, Trans. Amer. Math. Soc. 108 (1963), 275-292, 293-312. https://doi.org/10.2307/1993608
  11. K. Varadarajan, Genralized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
  12. M. H. Woo and Y. S. Yoon, T-spaces by the Gottlieb groups and duality, J. Austral. Math. Soc. (Series A) 59 (1995), 193-203. https://doi.org/10.1017/S1446788700038593
  13. Y. S. Yoon, The generalized dual Gottlieb sets, Top. Appl. 109 (2001), 173-181. https://doi.org/10.1016/S0166-8641(99)00150-9
  14. Y. S. Yoon, $H^{f}$-spaces for maps and their duals, J. Korea Soc. Math. Educ. Ser. B 14 (2007), no. 4, 289-306.
  15. Y. S. Yoon, Lifting T-structures and their duals, J. Chungcheong Math. Soc. 20 (2007), no. 3, 245-259.
  16. Y. S. Yoon, On cocyclic maps and cocategory, J. Chungcheong Math. Soc. 24 (2011), no. 1, 137-140.

Cited by

  1. CATEGORY OF MAPS AND GOTTLIEB SETS FOR MAPS, AND THEIR DUALS vol.26, pp.1, 2013, https://doi.org/10.14403/jcms.2013.26.1.249
  2. WEAK Cfk-SPACES FOR MAPS AND THEIR DUALS vol.27, pp.1, 2014, https://doi.org/10.14403/jcms.2014.27.1.47