Bounded cohomology of lattices in higher rank Lie groups

@article{Burger1999BoundedCO,
  title={Bounded cohomology of lattices in higher rank Lie groups
},
  author={M. Burger and Nicolas Monod},
  journal={Journal of the European Mathematical Society},
  year={1999},
  volume={1},
  pages={199-235}
}
  • M. Burger, N. Monod
  • Published 30 June 1999
  • Mathematics
  • Journal of the European Mathematical Society
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… 
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