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The Novikov Conjecture for Linear Groups

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Hawai‘i, Manoa, 2565 McCarthy Mall, Honolulu, HI, 96822-2273, USA

    Erik Guentner

  2. Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA

    Nigel Higson

  3. Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL, 60637, USA

    Shmuel Weinberger

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  1. Erik Guentner
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  2. Nigel Higson
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  3. Shmuel Weinberger
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Correspondence to Nigel Higson.

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Guentner, E., Higson, N. & Weinberger, S. The Novikov Conjecture for Linear Groups. Publ.math.IHES 101, 243–268 (2005). https://doi.org/10.1007/s10240-005-0030-5

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