# Bounded cohomology of lattices in higher rank Lie groups

Journal of the European Mathematical Society (1999)

- Volume: 001, Issue: 2, page 199-235
- ISSN: 1435-9855

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topBurger, 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 -

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