Bounded cohomology of lattices in higher rank Lie groups |
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Authors: | M. Burger N. Monod |
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Affiliation: | ETHZ, Department of Mathematics, R?mistrasse 101, CH-8092 Zürich, Switzerland, e-mail: {burger,monod}@math.ethz.ch, CH
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Abstract: | We prove that the natural map Hb 2(Γ)?H2(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 C1–action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating Hb •(Γ) to the continuous bounded cohomology of the ambient group with coefficients in some induction module. Received July 14, 1998 / final version received January 7, 1999 |
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