Mathematical Research Letters

Volume 14, Issue 4, July 2007 pp. 681-687.

Vanishing up to the rank in bounded cohomology

Authors: Nicolas Monod
Author institution: Université de Genève

Summary: We establish the vanishing for non-trivial unitary representations of the bounded cohomology of $\SL_d$ up to degree $d-1$. It holds more generally for uniformly bounded representations on superreflexive spaces. The same results are obtained for lattices. We also prove that the real bounded cohomology of any lattice is invariant in the same range.

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