Replacing homotopy actions by topological actions. II

Author:
Larry Smith

Journal:
Trans. Amer. Math. Soc. **317** (1990), 83-90

MSC:
Primary 57S99; Secondary 55P10

MathSciNet review:
976363

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Abstract: A homotopy action of a group on a space is a homomorphism from to the group of homotopy classes of homotopy equivalences of . George Cooke developed an obstruction theory to determine if a homotopy action is equivalent up to homotopy to a topological action. The question studied in this paper is: Given a diagram of spaces with homotopy actions of and maps between them that are equivariant up to homotopy, when can the diagram be replaced by a homotopy equivalent diagram of -spaces and -equivariant maps? We find that the obstruction theory of Cooke has a natural extension to this context.

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DOI:
http://dx.doi.org/10.1090/S0002-9947-1990-0976363-3

Article copyright:
© Copyright 1990
American Mathematical Society