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

García-Prada, Oscar; Toledo, Domingo

doi:10.2140/gt.2011.15.1013

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

Oscar García-Prada and Domingo Toledo

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 2000

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

Oscar García-Prada
Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM Serrano, 121 28006 - Madrid Spain
http://www.mat.csic.es/webpages/garcia-prada
Domingo Toledo
Department of Mathematics University of Utah Salt Lake City, UT 84112 USA
http://www.math.utah.edu/~toledo

Volume 15, issue 2 (2011)