Math Seminars.
Marc Burger
Introduction to Bounded Cohomology
We introduce bounded continuous cohomology of locally compact groups and
give a
functorial caracterization of it. We'll show how amenable actions in the
sense of Zimmer
play a fundamental role, in that they lead to resolutions allowing the
compution of these
cohomology groups in low degrees. We will then apply these techniques to
get rigidity
results on actions of lattices by diffeomorphisms on the circle, and
deformation rigidity
results concerning lattices in complex hyperbolic spaces.