Journal of the European Mathematical Society


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Volume 1, Issue 2, 1999, pp. 199–235
DOI: 10.1007/s100970050007

Published online: 1999-06-30

Bounded cohomology of lattices in higher rank Lie groups

Marc Burger[1] and Nicolas Monod[2]

(1) ETH Zürich, Switzerland
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland

We prove that the natural map Hb2(&)‘H2(&) 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 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”(&) to the continuous bounded cohomology of the ambient group with coefficients in some induction module.

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Burger Marc, Monod Nicolas: Bounded cohomology of lattices in higher rank Lie groups. J. Eur. Math. Soc. 1 (1999), 199-235. doi: 10.1007/s100970050007