Geodesic
Bounded cohomology of lattices in higher rank Lie groups
Journal of the European Mathematical Society, Tome 1 (1999) no. 2, pp. 199-235.

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We prove that the natural map Hb2​(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.
DOI : 10.1007/s100970050007
Classification : 22-XX, 00-XX
Keywords: 
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     author = {Marc Burger and Nicolas Monod},
     title = {Bounded cohomology of lattices in higher rank {Lie} groups},
     journal = {Journal of the European Mathematical Society},
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Marc Burger; Nicolas Monod. Bounded cohomology of lattices in higher rank Lie groups. Journal of the European Mathematical Society, Tome 1 (1999) no. 2, pp. 199-235. doi : 10.1007/s100970050007. http://geodesic.mathdoc.fr/articles/10.1007/s100970050007/

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