Gp-SPACES FOR MAPS AND HOMOLOGY DECOMPOSITIONS

Title & Authors
Gp-SPACES FOR MAPS AND HOMOLOGY DECOMPOSITIONS
Yoon, Yeon Soo;

Abstract
For a map $\small{p:X{\rightarrow}A}$, we define and study a concept of $\small{G^{\prime}_p}$-space for a map, which is a generalized one of a G-space. Any G-space is a $\small{G^{\prime}_p}$-space, but the converse does not hold. In fact, $\small{CP^2}$ is a $\small{G^{\prime}_{\delta}}$-space, but not a G`-space. It is shown that X is a $\small{G^{\prime}_p}$-space if and only if $G^n(X,p,A) Keywords $\small{G^f}$-spaces for maps;Postnikov systems; Language English Cited by References 1. J. Aguade, Decomposable free loop spaces, Canad. J. Math. 39 (1987), 938-955. 2. B. Eckmann and P. Hilton, Decomposition homologique d'un polyedre simplement connexe, Canad. J. Math. 248 (1959), 2054-2558. 3. D. H. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856. 4. D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. 5. Marek Golansinski and John R. Klein, On maps into a co-H-space, Hiroshima Math. J. 28 (1998), 321-327. 6. H. B. Haslam, G-spaces and H-spaces, Ph. D. Thesis, Univ. of California, Irvine, 1969. 7. P. Hilton, Homotopy Theory and Duality, Gordon and Breach Science Pub., 1965. 8. D. W. Kahn, Induced maps for Postnikov systems, Trans. Amer. Math. Soc. 107 (1963), 432-450. 9. D. W. Kahn, A note on H-spaces and Postnikov systems of spheres, Proc. Amer. Math. Soc. 15 (1964), 300-307. 10. K. L. Lim, On cyclic maps, J. Austral. Math. Soc. (Series A) 32 (1982), 349-357. 11. K. L. Lim, Cocyclic maps and coevaluation subgroups, Canad. Math. Bull. 30 (1987), 63-71. 12. Christopher McCord and John Oprea, Rational Ljusternik-Schnirelmann Category and the Arnol'd conjecture for nilmanifolds, Topology 32 (1993), no. 4, 701-717. 13. N. Oda, The homotopy of the axes of pairings , Canad. J. Math. 17 (1990), 856-868. 14. Graham Hilton Toomer, Liusternik-Schnirelmann Category and the Moore spectral sequence, Ph. D. dissertation, Cornell University, 1974. 15. Graham Hilton Toomer, Two applications of homology decompositions, Can. J. Math. 27 (1975), no. 2, 323-329. 16. K. Varadarajan, Genralized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164. 17. G. W. Whitehead, Elements of homotopy theory, Springer-Verlag, New York Inc., 1978. 18. 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. 19. Y. S. Yoon, Lifting Gottlieb sets and duality, Proc. Amer. Math. Soc. 119 (1993), no. 4, 1315-1321. 20. Y. S. Yoon, The generalized dual Gottlieb sets, Topology Appl. 109 (2001), 173-181. 21. Y. S. Yoon,$G^f$-spaces for maps and Postnikov systems, J. Chungcheong Math. Soc. 22 (2009), no. 4, 831-841. 22. Y. S. Yoon,$H^f\$-spaces for maps and thier duals, J. Korean Soc. Math. Educ. Ser. B. 14 (2007), no. 4, 289-306.

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