Abstract
We prove the strong Atiyah conjecture for right-angled Artin groups and right-angled Coxeter groups. More generally, we prove it for groups which are certain finite extensions or elementary amenable extensions of such groups.
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Atiyah, M.F.: Elliptic operators, discrete groups and von Neumann algebras, Colloque “Analyse etTopologie” en l’Honneur de Henri Cartan (Orsay, 1974), Soc. Math. France, Paris, pp. 43–72. Astérisque, No. 32–33, (1976). MR 0420729 (54 #8741)
Austin, T.: Rational group ring elements with kernels having irrational dimension (2009). arXiv:0909.2360
Davis, M.W.: The Geometry and Topology of Coxeter Groups, London Mathematical Society Monographs Series, vol. 32. Princeton University Press, Princeton (2008). MR 2360474 (2008k:20091)
Davis M.W., Januszkiewicz T.: Right-angled Artin groups are commensurable with right-angled Coxeter groups. J. Pure Appl. Algebra 153(3), 229–235 (2000). doi:10.1016/S0022-4049(99)00175-9 MR 1783167 (2001m:20056)
Davis M.W., Okun B.: Vanishing theorems and conjectures for the l 2-homology of right-angled Coxeter groups. Geom. Topol. 5, 7–74 (2001) MR 1812434 (2002e:58039)
Dodziuk J., Linnell P., Mathai V., Schick T., Yates S.: Approximating L 2-invariants and the Atiyah conjecture. Comm. Pure Appl. Math. 56(7), 839–873 (2003). doi:10.1002/cpa.10076 Dedicated to the memory of Jürgen K. Moser. MR 1990479 (2004g:58040)
Duchamp, G., Krob, D., The lower central series of the free partially commutative group Semigroup Forum 45(3), 385–394 (1992). doi:10.1007/BF03025778. MR 1179860 (93e:20047)
Grabowski, L.: On Turing machines, dynamical systems and the Atiyah problem (2010). arXiv:1004.2030
Linnell P.A.: Division rings and group von Neumann algebras. Forum Math. 5(6), 561–576 (1993). doi:10.1515/form.1993.5.561. MR 1242889 (94h:20009)
Linnell, P., Schick, T.: Finite group extensions and the Atiyah conjecture. J. Am. Math. 20(4), 1003–1051 (2007) (electronic), doi:10.1090/S0894-0347-07-00561-9 MR 2328714 (2008m:58041)
Lorensen K.: Groups with the same cohomology as their pro-p completions. J. Pure Appl. Algebra 214(1), 6–14 (2010). doi:10.1016/j.jpaa.2009.04.002 MR 2561762 (2010k:20088)
Pichot, M., Schick, T., Zuk, A.: Closed manifolds with transcendental L2-Betti numbers (2010). arXiv:1005.1147
Schick T.: Integrality of L 2-Betti numbers. Math. Ann. 317(4), 727–750 (2000). doi:10.1007/PL00004421 Erratum in, Vol. 322, 421–422. MR 1777117 (2002k:55009a)
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Linnell, P., Okun, B. & Schick, T. The strong Atiyah conjecture for right-angled Artin and Coxeter groups. Geom Dedicata 158, 261–266 (2012). https://doi.org/10.1007/s10711-011-9631-y
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DOI: https://doi.org/10.1007/s10711-011-9631-y