Bounded Cohomology and Deformation Rigidity in Complex Hyperbolic Geometry

Details Bounded Cohomology and Deformation Rigidity in Complex Hyperbolic Geometry Bounded Cohomology and Deformation Rigidity in Complex Hyperbolic Geometry

2005-05-04

arxiv.org/abs/math/0505069v1

Mathematics

Metric Geometry

56 pages, 2 figures

Scientific paper

We develop further basic tools in the theory of continuous bounded cohomology of locally compact groups. We apply this tools to establish a Milnor-Wood type inequality in a very general context and to prove a global rigidity result which was originally announced by the authors with a sketch of a proof using bounded cohomology techniques and then proven by Koziarz and Maubon using harmonic map techniques. As a corollary one obtains that a lattice in SU(p,1) cannot be deformed nontrivially in SU(q,1), if either p is at least 2 or the lattice is cocompact. This generalizes to noncocompact lattices a theorem of Goldman and Millson.

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