Diffeomorphism Groups of Compact 4-manifolds are not always Jordan

2014/11/27 by Balázs Csikós, Csikós, Balázs, László Pyber +3 · 2 citations
Mathematics · #54H15 #57S17 #Advanced Combinatorial Mathematics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1411.7524

openalex publication_date 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that if M is a compact smooth manifold diffeomorphic to the total space of an orientable S² bundle over the torus T², then its diffeomorphism group does not have the Jordan property, i.e., Diff(M) contains a finite subgroup G_n for any natural number n such that every abelian subgroup of G_n has index at leat n. This gives a counterexample to an old conjecture of Ghys.

Citations

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

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