Replacing homotopy actions by topological actions

Cooke, George

doi:10.1090/S0002-9947-1978-0461544-2

Replacing homotopy actions by topological actions
HTML articles powered by AMS MathViewer

by George Cooke

Trans. Amer. Math. Soc. 237 (1978), 391-406

DOI: https://doi.org/10.1090/S0002-9947-1978-0461544-2

PDF | Request permission

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

J. F. Adams, A variant of E. H. Brown’s representability theorem, Topology 10 (1971), 185–198. MR 283788, DOI 10.1016/0040-9383(71)90003-6
Guy Allaud, On the classification of fiber spaces, Math. Z. 92 (1966), 110–125. MR 189035, DOI 10.1007/BF01312430
A. K. Bousfield, The localization of spaces with respect to homology, Topology 14 (1975), 133–150. MR 380779, DOI 10.1016/0040-9383(75)90023-3
A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573

Constructing spaces with interesting

cohomology via

actions on loop spaces

Peter Hilton, Homotopy theory and duality, Gordon and Breach Science Publishers, New York-London-Paris, 1965. MR 0198466
James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246. MR 154286, DOI 10.1016/0040-9383(63)90006-5
Dennis Sullivan, Geometric topology. Part I, Massachusetts Institute of Technology, Cambridge, Mass., 1971. Localization, periodicity, and Galois symmetry; Revised version. MR 0494074