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

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 t...

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Bibliographic Details
Published inarXiv.org
Main Author Riera, Ignasi Mundet i
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.03.2019
Subjects
Automorphisms
Homology
Manifolds
Mathematics - Differential Geometry
Mathematics - Group Theory
Subgroups
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1403.0383