Finite subgroups of diffeomorphism groups

Abstract

We prove:(1) the existence, for every integer n > 3, of a noncompact smooth n-dimensional topological manifold whose diffeomorphism group contains an isomorphic copy of every finitely presented group; (2) a finiteness theorem on finite simple subgroups of diffeomorphism groups of compact smooth topological manifolds.

7 pages. Several minor corrections and updates are made, and the sketch of proof of Theorem 2 is replaced by a complete proof

References in corpus (2)

• Finite group actions on manifolds without odd cohomology
• Jordan groups and automorphism groups of algebraic varieties

Cited by in corpus (5)

• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
• Finite group actions on manifolds without odd cohomology
• Non Jordan groups of diffeomorphisms and actions of compact Lie groups on manifolds
• Finite group actions on 4-manifolds with nonzero Euler characteristic
• On Jordan type bounds for finite groups of diffeomorphisms of 3-manifolds and Euclidean spaces