4 M ay 2 00 5 BOUNDED COHOMOLOGY AND DEFORMATION RIGIDITY IN COMPLEX HYPERBOLIC GEOMETRY
نویسنده
چکیده
We develop further basic tools in the theory of bounded continuous cohomology of locally compact groups; as such, this paper can be considered a sequel to [18], [39], and [11]. We apply these tools to establish a Milnor–Wood type inequality in a very general context and to prove a global rigidity result which was originally announced in [13] and [33] with a sketch of a proof using bounded cohomology techniques and then proven by Koziarz and Maubon in [36] using harmonic map techniques. As a corollary one obtains that a lattice in SU(p, 1) cannot be deformed nontrivially in SU(q, 1), q ≥ p, if either p ≥ 2 or the lattice is cocompact. This generalizes to noncocompact lattices a theorem of Goldman and Millson, [29].
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