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

García-Prada, Oscar¹ ; Toledo, Domingo²

¹ Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Serrano, 121, 28006 - Madrid, Spain
² Department of Mathematics, University of Utah, Salt Lake City, UT 84112 USA

Geometry & topology, Tome 15 (2011) no. 2, pp. 1013-1027.

Résumé

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.

Détail

DOI : 10.2140/gt.2011.15.1013

Keywords: Milnor–Wood inequality, rigidity, complex hyperbolic lattice

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