Groups of small homological dimension and the Atiyah Conjecture

Peter Kropholler; Peter Linnell; Wolfgang Lueck

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Groups of small homological dimension and the Atiyah Conjecture

Peter Kropholler·Peter Linnell·Wolfgang Lueck

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Abstract

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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BibTeX RIS

Peter Kropholler, Peter Linnell, Wolfgang Lueck. 2004-01-23. Groups of small homological dimension and the Atiyah Conjecture. https://arxiv.org/abs/math/0401312

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