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The Novikov Conjecture for Linear Groups, written jointly with N. Higson and S. Weinberger

This paper will appear in Publications Mathematiques de l'IHES.

Abstract (paraphrased from the preprint)

Let K be a field. We show that every countable subgroup of GL(n,K) is uniformly embeddable in a Hilbert space; indeed, we show that such groups are exact, in the sense of C*-algebra theory. 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. We conclude with an application to the problem of homotopy invariance of relative eta invariants.