The Novikov Conjecture for Linear Groups |
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| Authors: | Erik Guentner Nigel Higson Shmuel Weinberger |
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| Affiliation: | (1) Department of Mathematics, University of Hawai‘i, Manoa, 2565 McCarthy Mall, Honolulu, HI 96822-2273, USA;(2) Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;(3) Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA |
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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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