L 2-Betti numbers of one-relator groups
نویسندگان
چکیده
منابع مشابه
“ L 2 - Betti numbers of mapping tori and groups ” by
We prove the following two conjectures of Gromov. Firstly, all L2-Betti numbers of a manifold fibered over S1 are trivial. Secondly, the first L2-Betti number of a finitely presented group Γ vanishes provided that Γ is an extension {1} −→ ∆ −→ Γ −→ π −→ {1} of finitely presented groups such that ∆ is infinite and π contains Z as a subgroup. We conclude for such a group Γ that its deficiency is ...
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Uniform spanning trees on finite graphs and their analogues on infinite graphs are a well-studied area. On a Cayley graph of a group, we show that they are related to the first l-Betti number of the group. Our main aim, however, is to present the basic elements of a higher-dimensional analogue on finite and infinite CW-complexes, which relate to the higher l-Betti numbers. One consequence is a ...
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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 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 ...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2006
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-006-0058-y