منابع مشابه
Integrality of L2-Betti numbers
The Atiyah conjecture predicts that the L-Betti numbers of a finite CW -complex with torsion-free fundamental group are integers. We establish the Atiyah conjecture, under the condition that it holds for G and that H G is a normal subgroup, for amalgamated free products G ∗H (H ⋊ F ). Here F is a free group and H ⋊ F is an arbitrary semi-direct product. This includes free products G∗F and semi-...
متن کاملIntegrality of L-Betti numbers
The Atiyah conjecture predicts that the L-Betti numbers of a finite CW -complex with torsion-free fundamental group are integers. We show that the Atiyah conjecture holds (with an additional technical condition) for direct and inverse limits of directed systems of groups for which it is true. As a corollary it holds for residually torsion-free solvable groups, e.g. for pure braid groups or for ...
متن کاملL2-betti Numbers of Discrete Measured Groupoids
There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II 1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück’s dimension theory, Gaboriau’s definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition...
متن کاملOn the Definition of L2-Betti Numbers of Equivalence Relations
We show that the L-Betti numbers of equivalence relations defined by R. Sauer coincide with those defined by D. Gaboriau.
متن کاملVolume and L2-Betti numbers of aspherical manifolds
We give a leisurely account of the relationship between volume and L2-Betti numbers on closed, aspherical manifolds based on the results in [4] – albeit with a different point of view. This paper grew out of a talk presented at the first colloquium of the Courant Center in Göttingen in October 2007. 1. Review of L2-Betti numbers The L2-Betti numbers of a closed Riemannian manifold, as introduce...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2002
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s002080100282