Vanishing up to the rank in bounded cohomology

Details Vanishing up to the rank in bounded cohomology Vanishing up to the rank in bounded cohomology

2006-12-12

arxiv.org/abs/math/0612302v1

See final version in: Math Res Letters 14 No. 4 (2007) 681--687

Mathematics

Group Theory

5 pages

Scientific paper

We establish the vanishing for non-trivial unitary representations of the
bounded cohomology of SL_d up to the rank. 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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