Bounded cohomology of lattices in higher rank Lie groups

Let G be an irreducible uniform lattice in a higher semi-simple
rank Lie group or algebraic group. We prove that any G-action on the
circle by C^{1} diffeomorphisms is finite. This is achieved by showing that
natural map from
bounded to usual second cohomology is injective. The latter holds also for
non-trivial unitary coefficients, and implies more finiteness results for
G; for instance the stable commutator length vanishes. We prove the
same theorems for certain lattices in products of trees.

**Note:** In case of rank one factors, see this Erratum.

Bibliographical: J. Eur. Math. Soc.

Download: published pdf | preprint pdf

[Publications][Nicolas Monod]