Free subgroups in a mapping class group

Koji Fujiwara, Tohoku University

Generalizing a construction of quasi-homomorphisms on a group acting
on hyperbolic spaces, we construct quasi-homomorphisms on a group
acting on a CAT(0)-space with rank-1 isometries.  As an application,
we characterize finite volume, locally symmetric spaces of rank at
least two among finite volume complete Riemannian manifolds of
non-positive curvature using quasi-homomorphisms on the fundamental
groups.

The construction also applies to the action of a mapping class group
on the Teichmuller space with Weil-Petersson metric.  We show
pseudo-Anosov elements are rank-1 in our sense.

This is a joint work with Bestvina.