Stabilization of Bounded Cohomology for Classical Groups

We show that bounded cohomology stabilizes along sequences of classical real and complex Lie groups, and along sequences of lattices in them. Our method is based on a stability criterion which adapts Quillen's method to the setting of bounded cohomology. This criterion is then applied to a family of measured complexes, the so-called Stiefel complexes, associated to any vector space endowed with a non-degenerate sesquilinear form.