Fundamental groups of ergodic dynamical systems with invariant measure are considered.

We study the outer automorphism group OutRr of the ergodic equivalence relation Rr generated by the action of a lattice F in a semisimple Lie group on the homogeneos space of a compact group K. It is shown that OutRr is locally compact. If K is a connected simple Lie group, we prove the compactness of 0\itR r using the D. Witte's rigidity theorem. Moreover, an example of an equivalence relation without outer automorphisms is constructed.

No abstract

No abstract

No abstract