Groups not acting on manifolds

David Fisher, Lior Silberman

Published 2008-01-06, updated 2008-05-15Version 3

In this article we collect a series of observations that constrain actions of many groups on compact manifolds. In particular, we show that "generic" finitely generated groups have no smooth volume preserving actions on compact manifolds while also producing many finitely presented, torsion free groups with the same property.