On the bounded cohomology of semi-simple groups, S-arithmetic groups and products

Abstract

We prove vanishing results for Lie groups and algebraic groups (over any local field) in bounded cohomology. The main result is a vanishing below twice the rank for semi-simple groups. Related rigidity results are established for S-arithmetic groups and groups over global fields. We also establish vanishing and cohomological rigidity results for products of general locally compact groups and their lattices.

References in corpus (2)

• On co-amenability for groups and von Neumann algebras
• Product groups acting on manifolds

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• Kadison-Kastler stable factors
• Parametrized Euler class and semicohomology theory
• Non-vanishing unitary cohomology of low-rank integral special linear groups
• Bounded cohomology and scl of verbal wreath products
• The space of non-extendable quasimorphisms