Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Lifting Gottlieb sets and duality


Author: Yeon Soo Yoon
Journal: Proc. Amer. Math. Soc. 119 (1993), 1315-1321
MSC: Primary 55P05; Secondary 55R05
MathSciNet review: 1184089
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ p:{E_f} \to X$ be a fibration induced by a map $ f:X \to Y$ from the path space fibration $ \varepsilon :PY \to Y$. Let $ g:A \to X$ be cyclic. When does $ g$ lift to a map $ A \to {E_f}$ which is cyclic? We give an answer of this question for arbitrary $ A$ and $ Y$. Also, we give an answer in the dual situation.


References [Enhancements On Off] (What's this?)

  • [1] D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. MR 0275424 (43:1181)
  • [2] I. G. Halbhavi and K. Varadarajan, Gottlieb sets and duality in homotopy theory, Canad. J. Math. 27 (1975), 1042-1055. MR 0391085 (52:11907)
  • [3] H. B. Haslam, $ G$-spaces and $ H$-spaces, Ph.D. dissertation, Univ. of California, Irvine, 1969.
  • [4] C. S. Hoo, Lifting Gottlieb sets, J. London Math. Soc. (2) 14 (1976), 535-544. MR 0438339 (55:11254)
  • [5] K. L. Lim, On cyclic maps, J. Austral. Math. Soc. Ser. A 32 (1982), 349-357. MR 652412 (83e:55003)
  • [6] R. M. Switzer, Algebraic topology--homotopy and homology, Springer-Verlag, New York, 1975. MR 0385836 (52:6695)
  • [7] K Tsuchida, Principal cofibrations, Tohuku Math. J. 16 (1964), 321-333. MR 0177415 (31:1678)
  • [8] K. Varadarajan, Generalized Gottlieb groups, J. Indian Math. Soc. 33 (1969), 141-164. MR 0281207 (43:6926)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 55P05, 55R05

Retrieve articles in all journals with MSC: 55P05, 55R05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1184089-7
Keywords: Cyclic maps, cocyclic maps, principal fibrations, principal cofibrations
Article copyright: © Copyright 1993 American Mathematical Society