2010-11-19

Domingo Toledo, University of Utah

A Milnor-Wood inequality for complex hyperbolic lattices in quaternionic space

This talk will review some of the generalizations of the original Milnor-Wood inequality, partiicularly in relation to the bounded cohomology of Lie groups. Then we will prove a Milnor - Wood inequality for representations of a lattice in SU(m,1) in the group Sp(n,1) of isometries of quaternionic hyperbolic space. The case of equality has applications to rigidity questions. It gives global rigidity theorems that are related to recent local rigidity results of Kim-Pansu and Klingler. We will also discuss some conjectural related inequalities. This is joint work with Oscar Garcia Prada.