3 papers
math.DS2012
Volume-preserving actions of simple algebraic Q-groups on low-dimensional manifolds
Dave Witte Morris, Robert J. Zimmer
We prove that SL(n,Q) has no nontrivial, C-infinity, volume-preserving action on any compact manifold of dimension strictly less than n. More generally, suppose G is a connected, i…
math.DS2007
Invariant rigid geometric structures and smooth projective factors
Amos Nevo, Robert J. Zimmer
We consider actions of non-compact simple Lie groups preserving an analytic rigid geometric structure of algebraic type on a compact manifold. The structure is not assumed to be un…
math.DG2002
Ergodic actions of semisimple Lie groups on compact principal bundles
Dave Witte, Robert J. Zimmer
Let G = SL(n,R) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a…