Mathematical Research Letters
Volume 14 (2007)
Vanishing up to the rank in bounded cohomology
Pages: 681 – 687
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.