Gromov's centralizer theorem (Q1412318)

M. Gromov's centralizer theorem states that whenever a simple group acts on a compact manifold preserving a finite measure and a suitable rigid structure, the universal cover of the manifold has a space of killing fields centralizing the action and generating orbits at least as large as those of the group. The authors give a complete proof of the above theorem and an extension of it to finite volume manifolds which are not necessarily compact.