Galois cohomology of completed link groups
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- by Inga Blomer, Peter A. Linnell and Thomas Schick PDF
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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
- MR Author ID: 114455
- Email: linnell@math.vt.edu
- Thomas Schick
- Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstr. 3-5, 37073 Göttingen, Germany
- MR Author ID: 635784
- Email: schick@uni-math.gwdg.de
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3449-3459
- MSC (2000): Primary 20E18; Secondary 20J06, 57M25
- DOI: https://doi.org/10.1090/S0002-9939-08-09395-7
- MathSciNet review: 2415028