Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Replacing homotopy actions by topological actions


Author: George Cooke
Journal: Trans. Amer. Math. Soc. 237 (1978), 391-406
MSC: Primary 57E99; Secondary 55D10
DOI: https://doi.org/10.1090/S0002-9947-1978-0461544-2
MathSciNet review: 0461544
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A homotopy action of a group G on a space X is a homomorphism from G to the group of homotopy classes of homotopy equivalences of X. The question studied in this paper is: When is a homotopy action equivalent, in an appropriate sense, to a topological action of G on X?


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

  • [1] J. F. Adams, A variant of E. H. Brown's representability theorem, Topology 10 (1971), 185-198. MR 0283788 (44:1018)
  • [2] Guy Allaud, On the classification of fibre spaces, Math. Z. 92 (1966), 110-125. MR 0189035 (32:6462)
  • [3] A. K. Bousfield, The localization of a space with respect to homology, Topology 14 (1975), 133-150. MR 0380779 (52:1676)
  • [4] A. K. Bousfield and D. M. Kan, Homotopy limits, completions, and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, Berlin and New York, 1972. MR 0365573 (51:1825)
  • [5] G. E. Cooke, Constructing spaces with interesting $ {Z_p}$-cohomology via $ \varepsilon $-actions on loop spaces, Cornell Univ. (preprint).
  • [6] P. Hilton, Homotopy theory and duality, Gordon & Breach, New York, 1965. MR 0198466 (33:6624)
  • [7] James D. Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239-246. MR 0154286 (27:4235)
  • [8] D. Sullivan, Geometric topology, Part I: Localization,periodicity, and Galois symmetry, M.I.T. Press, Cambridge, Mass., 1970. MR 0494074 (58:13006a)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57E99, 55D10

Retrieve articles in all journals with MSC: 57E99, 55D10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1978-0461544-2
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society