Galois cohomology of completed link groups
Group Theory
2008-12-08 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.0708.3727,
title = {Galois cohomology of completed link groups},
author = {Inga Blomer and Peter Linnell and Thomas Schick},
journal= {arXiv preprint arXiv:0708.3727},
year = {2008}
}
Comments
11 pages, AMS-LaTeX 2e, v2 to appear in Proc.Amer.Math.Soc., minor corrections