Voir la notice de l'article provenant de la source Numdam
Let be a field. We show that every countable subgroup of is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of is exact, in the sense of -algebra theory.
@article{PMIHES_2005__101__243_0,
author = {Guentner, Erik and Higson, Nigel and Weinberger, Shmuel},
title = {The {Novikov} conjecture for linear groups},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {243--268},
publisher = {Springer},
volume = {101},
year = {2005},
doi = {10.1007/s10240-005-0030-5},
mrnumber = {2217050},
zbl = {1073.19003},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10240-005-0030-5/}
}
TY - JOUR AU - Guentner, Erik AU - Higson, Nigel AU - Weinberger, Shmuel TI - The Novikov conjecture for linear groups JO - Publications Mathématiques de l'IHÉS PY - 2005 SP - 243 EP - 268 VL - 101 PB - Springer UR - http://geodesic.mathdoc.fr/articles/10.1007/s10240-005-0030-5/ DO - 10.1007/s10240-005-0030-5 LA - en ID - PMIHES_2005__101__243_0 ER -
%0 Journal Article %A Guentner, Erik %A Higson, Nigel %A Weinberger, Shmuel %T The Novikov conjecture for linear groups %J Publications Mathématiques de l'IHÉS %D 2005 %P 243-268 %V 101 %I Springer %U http://geodesic.mathdoc.fr/articles/10.1007/s10240-005-0030-5/ %R 10.1007/s10240-005-0030-5 %G en %F PMIHES_2005__101__243_0
Guentner, Erik; Higson, Nigel; Weinberger, Shmuel. The Novikov conjecture for linear groups. Publications Mathématiques de l'IHÉS, Tome 101 (2005), pp. 243-268. doi: 10.1007/s10240-005-0030-5
Cité par Sources :