TY - JOUR
T1 - The Novikov conjecture for linear groups
AU - Guentner, Erik
AU - Higson, Nigel
AU - Weinberger, Shmuel
N1 - Funding Information:
The authors were partially supported by grants from the U.S. National Science Foundation.
PY - 2005/6
Y1 - 2005/6
N2 - 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.
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.
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U2 - 10.1007/s10240-005-0030-5
DO - 10.1007/s10240-005-0030-5
M3 - Article
AN - SCOPUS:23944466890
SN - 0073-8301
VL - 101
SP - 243
EP - 268
JO - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
JF - Publications Mathematiques de l'Institut des Hautes Etudes Scientifiques
IS - 1
ER -