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