On homomorphisms of groups into the Mapping class groups

This is a joint work with J. Behrstock and C. Drutu. We show that if a group G has infinitely many pairwise non-conjugate homomorphisms into a mapping class group of a surface, then G has a finite index subgroup (the index depends on the surface only) that acts non-trivially on a real tree. If G is finitely presented, then the real tree can be replaced by a simplicial tree.