Isovariant homotopy equivalences of manifolds with group actions
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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.References
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Additional Information
- Reinhard Schultz
- Affiliation: Department of Mathematics, University of California at Riverside, Riverside, California 92521
- MR Author ID: 157165
- Email: schultz@math.ucr.edu
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1363-1370
- MSC (2010): Primary 55P91, 57S17; Secondary 55R91
- DOI: https://doi.org/10.1090/proc/12795
- MathSciNet review: 3447686