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

Abstract

A recent preprint of Csikós, Pyber and Szabó (arXiv:1411.7524) proves that the diffeomorphism group of $T^2\times S^2$ is not Jordan. The purpose of this paper is to generalize the arguments of Csikós, Pyber and Szabó in order to obtain many other examples of compact manifolds whose diffeomorphism group fails to be Jordan. In particular we prove that for any $\epsilon >0$ there exist manifolds admitting effective actions of arbitrarily large $p$-groups $\Gamma$ all of whose abelian subgroups have at most $|\Gamma {|}^{\epsilon }$ elements. Finally, we also recover some results on nonexistence of effective actions of compact connected semisimple Lie group on manifolds.

arXiv comment14 pages

References in corpus (6)

• Finite group actions on homology spheres and manifolds with nonzero Euler characteristic
• Diffeomorphism Groups of Compact 4-manifolds are not always Jordan
• Finite group actions on manifolds without odd cohomology
• Finite subgroups of diffeomorphism groups
• Finite group actions on 4-manifolds with nonzero Euler characteristic
• Boosting an analogue of Jordan's theorem for finite groups

Cited by in corpus (4)

• Finite group actions on homology spheres and manifolds with nonzero Euler characteristic
• Finite groups acting symplectically on $T^2\times S^2$
• Isometry groups of closed Lorentz 4-manifolds are Jordan
• Special $p$-groups acting on compact manifolds