Groups not acting on manifolds

2008/01/06 by David Fisher, Fisher, David, Lior Silberman +1
Mathematics · #37C85 #53C24 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.DG #math.DS #math.GR #msc:37C85 #msc:53C24

paper · pdf · doi:10.48550/arxiv.0801.0875

References added, minor changes

openalex publication_date 2008/01/06 · arxiv created 2008/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume preserving actions on compact manifolds while also producing many finitely presented, torsion free groups with the same property.

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