  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.
