Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57S99, 55P10

Retrieve articles in all journals with MSC: 57S99, 55P10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1990-0976363-3
PII: S 0002-9947(1990)0976363-3
Article copyright: © Copyright 1990 American Mathematical Society