Geometry & Topology

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

Oscar García-Prada and Domingo Toledo

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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.

Article information

Source
Geom. Topol., Volume 15, Number 2 (2011), 1013-1027.

Dates
Received: 14 October 2010
Accepted: 3 January 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732310

Digital Object Identifier
doi:10.2140/gt.2011.15.1013

Mathematical Reviews number (MathSciNet)
MR2821569

Zentralblatt MATH identifier
1227.22011

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry

Keywords
Milnor–Wood inequality rigidity complex hyperbolic lattice

Citation

García-Prada, Oscar; Toledo, Domingo. A Milnor–Wood inequality for complex hyperbolic lattices in quaternionic space. Geom. Topol. 15 (2011), no. 2, 1013--1027. doi:10.2140/gt.2011.15.1013. https://projecteuclid.org/euclid.gt/1513732310


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