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arXiv · 1403.0383

Finite group actions on homology spheres and manifolds with nonzero Euler characteristic

Ignasi Mundet i Riera
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Abstract

Let $X$ be a smooth manifold belonging to one of these three collections: acyclic manifolds (compact or not, possibly with boundary), compact connected manifolds (possibly with boundary) with nonzero Euler characteristic, integral homology spheres. We prove that $Diff(X)$ is Jordan. This means that there exists a constant $C$ such that any finite subgroup $G$ of $Diff(X)$ has an abelian subgroup whose index in $G$ is at most $C$. Using a result of Randall and Petrie we deduce that the automorphism groups of connected, non necessarily compact, smooth real affine varieties with nonzero Euler characteristic are Jordan.

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Ignasi Mundet i Riera. 2014-03-03. Finite group actions on homology spheres and manifolds with nonzero Euler characteristic. https://doi.org/10.1112/topo.12100

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