Bounded cohomology of lattices in higher rank Lie groups
Journal of the European Mathematical Society, Tome 1 (1999) no. 2, pp. 199-235
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We prove that the natural map Hb2(Γ)→H2(Γ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ: the stable commutator length vanishes and any C1-action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating Hb∙(Γ) to the continuous bounded cohomology of the ambient group with coefficients in some induction module.
@article{JEMS_1999_1_2_a1,
author = {Marc Burger and Nicolas Monod},
title = {Bounded cohomology of lattices in higher rank {Lie} groups},
journal = {Journal of the European Mathematical Society},
pages = {199--235},
publisher = {mathdoc},
volume = {1},
number = {2},
year = {1999},
doi = {10.1007/s100970050007},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s100970050007/}
}
TY - JOUR AU - Marc Burger AU - Nicolas Monod TI - Bounded cohomology of lattices in higher rank Lie groups JO - Journal of the European Mathematical Society PY - 1999 SP - 199 EP - 235 VL - 1 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1007/s100970050007/ DO - 10.1007/s100970050007 ID - JEMS_1999_1_2_a1 ER -
%0 Journal Article %A Marc Burger %A Nicolas Monod %T Bounded cohomology of lattices in higher rank Lie groups %J Journal of the European Mathematical Society %D 1999 %P 199-235 %V 1 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1007/s100970050007/ %R 10.1007/s100970050007 %F JEMS_1999_1_2_a1
Marc Burger; Nicolas Monod. Bounded cohomology of lattices in higher rank Lie groups. Journal of the European Mathematical Society, Tome 1 (1999) no. 2, pp. 199-235. doi: 10.1007/s100970050007
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