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Bounded cohomology of lattices in higher rank Lie groups

Marc BurgerNicolas Monod — 1999

Journal of the European Mathematical Society

We prove that the natural map H b 2 ( Γ ) H 2 ( Γ ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ : the stable commutator length vanishes and any C 1 –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating H * b ( Γ ) to the continuous bounded cohomology of the ambient group...

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