A differentiable classification of certain locally free actions of Lie groups (Q1650017)

Locally free actions (that is, actions of a topological group on a manifold for which every isotropy group is a discrete subgroup) are of interest for several reasons, including the way in which they naturally produce potentially interesting examples of foliations. Here the setting considered is a Lie group \(L\) acting smoothly on a compact manifold \(M\) of dimension \(\dim(L)+1\), and the main results describe conditions on the action in terms of relations between characters of the adjoint action of the radical of \(L\) which guarantee that the action is the restriction to \(L\) of a locally free transitive smooth action of a larger containing Lie group. A second result is that even in non-amenable cases an invariant probability measure is found.