| Authors: | Erik Guentner, Nigel Higson and Shmuel Weinberger |
| Title: | The Novikov conjecture for linear groups |
| Publication Information: | Publ. Math. Inst. Hautes Etudes Sci. 101 (2005), 243-268 |
| 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. |