Replacing homotopy actions by topological actions. II
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- by Larry Smith PDF
- Trans. Amer. Math. Soc. 317 (1990), 83-90 Request permission
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.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 317 (1990), 83-90
- MSC: Primary 57S99; Secondary 55P10
- DOI: https://doi.org/10.1090/S0002-9947-1990-0976363-3
- MathSciNet review: 976363