2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75086We 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.56 pages, 2 figuresMetric GeometryGroup Theory57S; 53text