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Diffeomorphism Groups of Compact 4-manifolds are not always Jordan

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arxiv 1411.7524 v1 pith:GE4RPDKA submitted 2014-11-27 math.DG math.GR

Balázs Csikós , László Pyber , Endre Szabó This is my paper · ORCID
classification math.DGmath.GR
keywords compactdiffeomorphismjordansubgroupabelianalwaysbundleconjecture
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abstract

We show that if $M$ is a compact smooth manifold diffeomorphic to the total space of an orientable $S^2$ bundle over the torus $T^2$, 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.

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  1. Large and iterated finite group actions on manifolds admitting non-zero degree maps to nilmanifolds

    math.GT 2025-06 conditional novelty 7.0 of 10

    Manifolds with non-zero degree maps to nilmanifolds have controlled finite group actions, and a new iterated symmetry invariant forces rational cohomology rigidity over two-step nilmanifolds.

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