Finite subgroups of diffeomorphism groups

2013/10/24 by Vladimir L. Popov, Popov, Vladimir L.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.AG #math.AT #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1310.6548

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

arxiv created 2014/01/06 · arxiv updated 2014/01/07

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.

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