The Novikov conjecture for linear groups

Erik Guentner, Nigel Higson, Shmuel Weinberger

Research output: Contribution to journalArticlepeer-review

54 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)243-268
Number of pages26
JournalPublications Mathematiques de l'Institut des Hautes Etudes Scientifiques
Volume101
Issue number1
DOIs
StatePublished - Jun 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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