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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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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.
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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