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

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

2010-10-14

arxiv.org/abs/1010.3014v1

Mathematics

Differential Geometry

13 pages

Scientific paper

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.

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