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Isovariant homotopy equivalences of manifolds with group actions


Author: Reinhard Schultz
Journal: Proc. Amer. Math. Soc. 144 (2016), 1363-1370
MSC (2010): Primary 55P91, 57S17; Secondary 55R91
DOI: https://doi.org/10.1090/proc/12795
Published electronically: August 11, 2015
MathSciNet review: 3447686
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Abstract: Let $ f$ be an equivariant homotopy equivalence $ f$ of connected closed manifolds with smooth semifree actions of a finite group $ G$, and assume also that $ f$ is isovariant. The main result states that $ f$ is a homotopy equivalence in the category of isovariant mappings if the manifolds satisfy a Codimension $ \geq 3$ Gap Hypothesis; this is done by showing directly that $ f$ satisfies the criteria in the Isovariant Whitehead Theorem of G. Dula and the author. Examples are given to show the need for the hypotheses in the main result.


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Additional Information

Reinhard Schultz
Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
Email: schultz@math.ucr.edu

DOI: https://doi.org/10.1090/proc/12795
Received by editor(s): January 20, 2015
Received by editor(s) in revised form: March 17, 2015
Published electronically: August 11, 2015
Communicated by: Michael A. Mandell
Article copyright: © Copyright 2015 American Mathematical Society