The Novikov conjecture for linear groups

Erik Guentner; Nigel Higson; Shmuel Weinberger

Publications Mathématiques de l'IHÉS (2005)

  • Volume: 101, page 243-268
  • ISSN: 0073-8301

Abstract

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Let K be a field. We show that every countable subgroup of GL(n,K) 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 GL(2,K) 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 GL(n,K) is exact, in the sense of C*-algebra theory.

How to cite

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Guentner, Erik, Higson, Nigel, and Weinberger, Shmuel. "The Novikov conjecture for linear groups." Publications Mathématiques de l'IHÉS 101 (2005): 243-268. <http://eudml.org/doc/104211>.

@article{Guentner2005,
abstract = {Let K be a field. We show that every countable subgroup of GL(n,K) 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 GL(2,K) 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 GL(n,K) is exact, in the sense of C*-algebra theory.},
author = {Guentner, Erik, Higson, Nigel, Weinberger, Shmuel},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {Novikov conjecture; Baum-Connes map; uniform embeddability},
language = {eng},
pages = {243-268},
publisher = {Springer},
title = {The Novikov conjecture for linear groups},
url = {http://eudml.org/doc/104211},
volume = {101},
year = {2005},
}

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
PB - Springer
VL - 101
SP - 243
EP - 268
AB - Let K be a field. We show that every countable subgroup of GL(n,K) 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 GL(2,K) 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 GL(n,K) is exact, in the sense of C*-algebra theory.
LA - eng
KW - Novikov conjecture; Baum-Connes map; uniform embeddability
UR - http://eudml.org/doc/104211
ER -

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