The Novikov conjecture for linear groups
Publications Mathématiques de l'IHÉS, Tome 101 (2005), p. 243-268
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.
@article{PMIHES_2005__101__243_0,
     author = {Guentner, Erik and Higson, Nigel and Weinberger, Shmuel},
     title = {The Novikov conjecture for linear groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Springer},
     volume = {101},
     year = {2005},
     pages = {243-268},
     doi = {10.1007/s10240-005-0030-5},
     zbl = {1073.19003},
     mrnumber = {2217050},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_2005__101__243_0}
}
Guentner, Erik; Higson, Nigel; Weinberger, Shmuel. The Novikov conjecture for linear groups. Publications Mathématiques de l'IHÉS, Tome 101 (2005) pp. 243-268. doi : 10.1007/s10240-005-0030-5. http://www.numdam.org/item/PMIHES_2005__101__243_0/

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