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

Abstract

We prove a Milnor-Wood inequality for representations of the fundamental group of a compact complex hyperbolic manifold in the group of isometries of quaternionic hyperbolic space. Of special interest is the case of equality, and its application to rigidity. We show that equality can only be achieved for totally geodesic representations, thereby establishing a global rigidity theorem for totally geodesic representations.

13 pages

References in corpus (4)

• Maximal surface group representations in isometry groups of classical Hermitian symmetric spaces
• Surface group representations in PU(p,q) and Higgs bundles
• Higgs bundles and surface group representations in the real symplectic group
• Local quaternionic rigidity for complex hyperbolic lattices

Cited by in corpus (2)

• Volume invariant and maximal representations of discrete subgroups of Lie groups
• Toledo invariant of lattices in SU(2,1) via symmetric square