Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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PRINCIPAL COFIBRATIONS AND GENERALIZED CO-H-SPACES

  • Yoon, Yeon Soo (Department of Mathematics Education Hannam University)
  • Received : 2017.01.11
  • Accepted : 2017.01.20
  • Published : 2017.02.15
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Abstract

For a map $p:X{\rightarrow}A$, there are concepts of co-$H^p$-spaces, co-$T^p$-spaces, which are generalized ones of co-H-spaces [17,18]. For a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from $\imath:X^{\prime}{\rightarrow}cX^{\prime}$, we obtain some sufficient conditions to having extensions co-$H^{\bar{p}}$-structures and co-$T^{\bar{p}}$-structures on $C_r$ of co-$H^p$-spaces and co-$T^p$-structures on X respectively. We can also obtain some results about co-$H^p$-spaces and co-$T^p$-spaces in homology decompositions for spaces, which are generalizations of Golasinski and Klein's result about co-H-spaces.

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Acknowledgement

Supported by : Hannam University

References

  1. J. Aguade, Decomposable free loop spaces, Canad. J. Math. 39 (1987), 938-955. https://doi.org/10.4153/CJM-1987-047-9
  2. B. Eckmann and P. Hilton, Decomposition homologique d'un polyedre simplement connexe, Canad. J. Math. 248 (1959), 2054-2558.
  3. M. Golasinski and J. R. Klein, On maps into a co-H-spaces, Hiroshima Math. J. 28 (1998), 321-327.
  4. D. H. Gottlieb, A certain subgroup of the fundamental group, Amer. J. Math. 87 (1965), 840-856. https://doi.org/10.2307/2373248
  5. H. B. Haslam, G-spaces and H-spaces, Ph. D. Thesis, Univ. of California, Irvine, 1969.
  6. P. Hilton, Homotopy Theory and Duality, Gordon and Breach Science Pub. 1965.
  7. N. Iwase, Ganea's conjecture on LS-category, Bull. Londen Math. Soc. 30 (1998), no. 6, 623-634. https://doi.org/10.1112/S0024609398004548
  8. D. W. Kahn, A note on H-spaces and Postnikov systems of spheres, Proc. Amer. Math. Soc. 15 (1964), 300-307.
  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. N. Oda, The homotopy of the axes of pairings , Canad. J. Math. 17 (1990), 856-868.
  11. G. H. Toomer, Liusternik-Schnirelmann Category and the Moore spectral sequence, Ph. D. Thesis, Cornell Univ. 1974.
  12. G. H. Toomer, Two Applications of Homology Decompositions, Can. J. Math. 27 (1975), no. 2, 323-329. https://doi.org/10.4153/CJM-1975-039-1
  13. K. Varadarajan, Generalized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164.
  14. 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
  15. Y. S. Yoon, Lifting Gottlieb sets and duality, Proc. Amer. Math. Soc. 119 (1993), no. 4, 1315-1321. https://doi.org/10.1090/S0002-9939-1993-1184089-7
  16. Y. S. Yoon, The generalized dual Gottlieb sets, Topology Appl. 109 (2001), 173-181. https://doi.org/10.1016/S0166-8641(99)00150-9
  17. Y. S. Yoon, $H^f$-spaces for maps and their duals, J. Korea Soc. Math. Edu. Series B 14 (2007), no. 4, 287-306.
  18. Y. S. Yoon, Lifting T-structures and their duals, J. Chungcheong Math. Soc. 20 (2007), no. 3, 245-259.
  19. Y. S. Yoon, $G'_p$-spaces for maps and Homology Decompositions, J. Chungcheong Math. Soc. 28 (2015), no. 4, 603-614. https://doi.org/10.14403/jcms.2015.28.4.603
  20. Y. S. Yoon, Principal Fibrations and Generalized H-spaces, J. Chungcheong Math. Soc. 29 (2016), no. 1, 177-186. https://doi.org/10.14403/jcms.2016.29.1.177