Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Galois cohomology of completed link groups

Author(s): Inga Blomer; Peter A. Linnell; Thomas Schick
Journal: Proc. Amer. Math. Soc. 136 (2008), 3449-3459.
MSC (2000): Primary 20E18; Secondary 20J06, 57M25
Posted: May 16, 2008
MathSciNet review: 2415028
Retrieve article in: PDF

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Abstract: In this paper we compute the Galois cohomology of the pro- completion of primitive link groups. Here, a primitive link group is the fundamental group of a tame link in whose linking number diagram is irreducible modulo (e.g. none of the linking numbers is divisible by ).

The result is that (with $\mathbb{Z}/p\mathbb{Z}$ -coefficients) the Galois cohomology is naturally isomorphic to the $\mathbb{Z}/p\mathbb{Z}$ -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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