Groups of small homological dimension and the Atiyah Conjecture

Details Groups of small homological dimension and the Atiyah Conjecture Groups of small homological dimension and the Atiyah Conjecture

2004-01-23

arxiv.org/abs/math/0401312v1

Mathematics

Group Theory

5 pages

Scientific paper

A group G has homological dimension less or equal to 1 if it is locally free. We prove the converse provided that G satisfies the Atiyah Conjecture about L^2-Betti numbers. We also show that a finitely generated elementary amenable group G of cohomological dimension less or equal to 2 possesses a finite 2-dimensional model for BG and in particular that G is finitely presented and the trivial ZG-module Z has a 2-dimensional resolution by finitely generated free ZG-modules.

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