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Transactions of the American Mathematical Society

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



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 $ G$ on a space $ X$ is a homomorphism from $ G$ to the group $ {\operatorname{HAUT}}(X)$ of homotopy classes of homotopy equivalences of $ X$. 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 $ G$ and maps between them that are equivariant up to homotopy, when can the diagram be replaced by a homotopy equivalent diagram of $ G$-spaces and $ G$-equivariant maps? We find that the obstruction theory of Cooke has a natural extension to this context.

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Article copyright: © Copyright 1990 American Mathematical Society