2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/209679In 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.11 pages, AMS-LaTeX 2e, v2 to appear in Proc.Amer.Math.Soc., minor correctionsGroup TheoryAlgebraic Geometry20E18, 20J06, 57M25text