Bounded cohomology of lattices in higher rank Lie groups
Bounded cohomology of lattices in higher rank Lie groups
We prove that the natural map H^2_b(\Gamma)\to H^2(\Gamma) from bounded to usual cohomology is injective if \Gamma is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for \Gamma : the stable commutator length vanishes and any …