Galois cohomology of completed link groups

Details Galois cohomology of completed link groups Galois cohomology of completed link groups

2007-08-28

arxiv.org/abs/0708.3727v2

Proc. Amer. Math. Soc. 136 (2008), no. 10, 3449--3459.

Mathematics

Group Theory

11 pages, AMS-LaTeX 2e, v2 to appear in Proc.Amer.Math.Soc., minor corrections

Scientific paper

10.1090/S0002-9939-08-09395-7

In this paper we compute the Galois cohomology of the pro-p completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in the 3-sphere whose linking number diagram is irreducible modulo p (e.g. none of the linking numbers is divisible by p). The result is that (with Z/pZ-coefficients) the Galois cohomology is naturally isomorphic to the Z/pZ-cohomology of the discrete link group. The main application of this result is that for such groups the Baum-Connes conjecture or the Atiyah conjecture are true for every finite extension (or even every elementary amenable extension), if they are true for the group itself.

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