Isovariant homotopy equivalences of manifolds with group actions

Schultz, Reinhard

doi:10.1090/proc/12795

Isovariant homotopy equivalences of manifolds with group actions
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Proc. Amer. Math. Soc. 144 (2016), 1363-1370 Request permission

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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