Non Jordan groups of diffeomorphisms and actions of compact Lie groups\n on manifolds

2014/12/22 by Ignasi Mundet-i-Riera, Mundet-i-Riera, Ignasi · 2 citations
Mathematics · #54H15 #57S17 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1412.6964

openalex publication_date 2014/12/22 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

A recent preprint of Csik 'os, Pyber and Szab 'o (arXiv:1411.7524) proves\nthat the diffeomorphism group of T²\× S² is not Jordan. The purpose of\nthis paper is to generalize the arguments of Csik 'os, Pyber and Szab 'o in\norder to obtain many other examples of compact manifolds whose diffeomorphism\ngroup fails to be Jordan. In particular we prove that for any \ε>0\nthere exist manifolds admitting effective actions of arbitrarily large\np-groups \Γ all of whose abelian subgroups have at most\n|\Γ|^\ε elements. Finally, we also recover some results on\nnonexistence of effective actions of compact connected semisimple Lie group on\nmanifolds.\n

Citations

• Finite group actions on 4-manifolds with nonzero Euler characteristic

Cited by

• Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds
• Isometry groups of closed Lorentz 4-manifolds are Jordan

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