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arXiv · 1411.7524

Diffeomorphism Groups of Compact 4-manifolds are not always Jordan

Balázs Csikós·László Pyber·Endre Szabó
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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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Balázs Csikós, László Pyber, Endre Szabó. 2014-11-27. Diffeomorphism Groups of Compact 4-manifolds are not always Jordan. https://arxiv.org/abs/1411.7524

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