Galois cohomology of completed link groups

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 -coefficients) the Galois cohomology is naturally isomorphic to the -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.