Some Remarks Inspired by the C 0 Zimmer Program

In the mid 80’s when I just arrived in Chicago, Bob Zimmer was lecturing on his recent work showing how perturbations of isometric actions of Kazhdan groups were dynamically simple (preserve a measurable Riemannian metric) [Zi1]. The heady mixture of the beauty of the results, the audacity of the vision (this is really 0% of what should be true...), and Bob’s charisma and charm attracted me so that I still cannot but help think about the problem of what large discrete groups of Cat-isomorphisms of a manifold can conceivably look like.