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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A Milnor–Wood inequality for complex hyperbolic lattices in quaternionic space

Oscar García-Prada and Domingo Toledo

Geometry & Topology 15 (2011) 1013–1027
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