Weyl groups, descent systems and Betti numbers

-Betti Numbers of Locally Compact Groups

We introduce a notion of L-Betti numbers for locally compact, second countable, unimodular groups. We study the relation to the standard notion of L-Betti numbers of countable discrete groups for lattices. In this way, several new computations are obtained for countable groups, including lattices in algebraic groups over local elds, and Kac-Moody lattices. We also extend the vanishing of reduce...

-Betti numbers and non-unitarizable groups without free subgroups

We show that there exist non-unitarizable groups without non-abelian free subgroups. Both torsion and torsion free examples are constructed.

“ 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 ...

-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 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...

Coverings and Betti Numbers