Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

SPLITTING OFF Hf-SPACES AND THEIR DUALS

  • Yoon, Yeon Soo (Department of Mathematics Education Hannam University)
  • Received : 2014.09.30
  • Accepted : 2014.10.20
  • Published : 2014.11.15
Download PDF
⟨ Previous Next ⟩

Abstract

We obtain a splitting theorem which characterizes when a given space is a catesian product of an $H^f$-space, and also obtain a dual theorem for a co-$H^g$-space. Then we get Dula and Gottlieb's results as corollaries.

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. G. Dula and D. H. Gottlieb, Splitting off H-spaces and Conner-Raymond Splitting Theorem, J. Fac. Sci. Univ. Tokyo Sect. IA, Math. 37 (1990), 321-334.
  3. D. H. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856. https://doi.org/10.2307/2373248
  4. D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. https://doi.org/10.2307/2373349
  5. D. H. Gottlieb, Splitting off tori and the evaluation subgroup of the fundamental group, Israel. J. Math. 66 (1989), 216-222. https://doi.org/10.1007/BF02765893
  6. H. B. Haslam, G-spaces and H-spaces, Ph. D. Thesis, Univ. of California, Irvine, 1969.
  7. P. Hilton, Nilpotency and H-spaces, Topology 3 (1965), no. 3, 161-176. https://doi.org/10.1016/0040-9383(65)90074-1
  8. K. L. Lim, On cyclic maps, J. Austral. Math. Soc. (Series A) 32 (1982), 349-357. https://doi.org/10.1017/S1446788700024903
  9. K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), 63-71. https://doi.org/10.4153/CMB-1987-009-1
  10. J. W. Milnor, On spaces having the homotopy type of a CW complex, Trans. Amer. Math. Soc. 90 (1959), 272-280.
  11. N. Oda, The homotopy of the axes of pairings, Canad. J. Math. 17 (1990), 856-868.
  12. J. Stasheff, On homotopy abelian H-spaces, Proc. Camb. Phil. Soc. 57 (1961), 734. https://doi.org/10.1017/S0305004100035878
  13. J. Stasheff, A classification theorem for fiber spaces, Topology 2 (1963), 239-246. https://doi.org/10.1016/0040-9383(63)90006-5
  14. K. Varadarajan, Genralized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
  15. Y. S. Yoon, The generalized dual Gottlieb sets, Topology Appl. 109 (2001), 173-181. https://doi.org/10.1016/S0166-8641(99)00150-9
  16. Y. S. Yoon, Generalized Gottlieb groups and generalized Wang homomorphisms, Sci. Math. Japon. 55 (2002), no. 1, 139-148.
  17. Y. S. Yoon, $H^f$-spaces for maps and their duals, J. Korea Soc. Math. Educ. Ser. B 14 (2007), no. 4, 289-306.