%0 Journal Article
%T Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
%A Bal¨˘zs Csik¨®s
%A L¨˘szl¨® Pyber
%A Endre Szab¨®
%J Mathematics
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1411.7524v1