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 -