Geometry & Topology 15 (2011) 1013–1027

DOI: 10.2140/gt.2011.15.1013

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.

Keywords

Milnor–Wood inequality, rigidity, complex hyperbolic lattice

Mathematical Subject Classification

Primary: 22E40

Secondary: 53C26

References

Publication

Received: 14 October 2010
Accepted: 3 January 2011
Published: 22 June 2011
Proposed: Simon Donaldson
Seconded: Danny Calegari, Leonid Polterovich

Authors