Dynamical correspondences of $L^2$-Betti numbers
نویسندگان
چکیده
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-...
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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...
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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 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 positive 1-relator g...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2018
ISSN: 1661-7207
DOI: 10.4171/ggd/480