Zimmer program

Summary

The Zimmer program is the study of smooth actions of lattices in higher-rank semisimple Lie groups on compact manifolds. Its guiding idea is that such actions are very restricted. In low dimension they should be finite, and in general they should come from algebraic constructions. It extends the Margulis superrigidity theorem, which describes linear representations of these lattices, to actions by diffeomorphisms. Zimmer's conjecture is its best known test case.