Bounded cohomology of lattices in higher rank Lie groups

Burger, Marc, and Monod, Nicolas. "Bounded cohomology of lattices in higher rank Lie groups." Journal of the European Mathematical Society 001.2 (1999): 199-235. <http://eudml.org/doc/277174>.

@article{Burger1999,
abstract = {We prove that the natural map $H^2_\{\text\{b\}\}(\Gamma )\rightarrow H^2(\Gamma )$ from bounded to usual cohomology is injective if $\Gamma $ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for $\Gamma $: the stable commutator length vanishes and any $C^1$–action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating $H^*\{\text\{b\}\}(\Gamma )$ to the continuous bounded cohomology of the ambient group with coefficients in some induction module.},
author = {Burger, Marc, Monod, Nicolas},
journal = {Journal of the European Mathematical Society},
keywords = {Lie group; irreducible cocompact lattice; continuous bounded cohomology; hyperbolic group; Gromov norm; quasimorphism; locally finite tree; irreducible cocompact lattice; higher rank Lie group; locally compact groups},
language = {eng},
number = {2},
pages = {199-235},
publisher = {European Mathematical Society Publishing House},
title = {Bounded cohomology of lattices in higher rank Lie groups},
url = {http://eudml.org/doc/277174},
volume = {001},
year = {1999},
}

TY - JOUR
AU - Burger, Marc
AU - Monod, Nicolas
TI - Bounded cohomology of lattices in higher rank Lie groups
JO - Journal of the European Mathematical Society
PY - 1999
PB - European Mathematical Society Publishing House
VL - 001
IS - 2
SP - 199
EP - 235
AB - We prove that the natural map $H^2_{\text{b}}(\Gamma )\rightarrow H^2(\Gamma )$ from bounded to usual cohomology is injective if $\Gamma $ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for $\Gamma $: the stable commutator length vanishes and any $C^1$–action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating $H^*{\text{b}}(\Gamma )$ to the continuous bounded cohomology of the ambient group with coefficients in some induction module.
LA - eng
KW - Lie group; irreducible cocompact lattice; continuous bounded cohomology; hyperbolic group; Gromov norm; quasimorphism; locally finite tree; irreducible cocompact lattice; higher rank Lie group; locally compact groups
UR - http://eudml.org/doc/277174
ER -