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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Galois cohomology of completed link groups


Authors: Inga Blomer, Peter A. Linnell and Thomas Schick
Journal: Proc. Amer. Math. Soc. 136 (2008), 3449-3459
MSC (2000): Primary 20E18; Secondary 20J06, 57M25
Published electronically: May 16, 2008
MathSciNet review: 2415028
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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 $ S^3$ whose linking number diagram is irreducible modulo $ p$ (e.g. none of the linking numbers is divisible by $ p$).

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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Additional Information

Inga Blomer
Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany
Email: ingablomer@gmx.de

Peter A. Linnell
Affiliation: Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061-0123
Email: linnell@math.vt.edu

Thomas Schick
Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany
Email: schick@uni-math.gwdg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09395-7
PII: S 0002-9939(08)09395-7
Keywords: Link group, Lie algebra, Galois cohomology
Received by editor(s): September 4, 2007
Published electronically: May 16, 2008
Additional Notes: The third author was funded by the DAAD (German Academic Exchange Agency)
Communicated by: Martin Lorenz
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.