Related papers: Graphs of groups and the Atiyah conjecture for one…
We generalize the Atiyah problem on configurations and the related Atiyah--Sutcliffe conjectures 1 and 2 using finite graphs, configurations of points and tensors. Our conjectures are intriguing geometric inequalities, defined using the…
Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
This paper has been withdrawn by the author because Conjecture 1 is false. Please see arXiv:0901.2093 for a justification that Conjecture 1 is false. The other main results are also available from the above URL.
The main result is a general approximation theorem for normalised Betti numbers for Farber sequences of lattices in totally disconnected groups. Further, we contribute some computations and complements to the general theory of $L^2$-Betti…
This submission has been withdrawn at the request of the author.
This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.
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…
The paper is withdrawn due to some errors.
This paper has been withdrawn by arXiv administrators because of disputed claims of authorship among former collaborators
The paper was withdrawn due to a gap in the proof of Lemma 3.
We reconsider work of Elkalla on subnormal subgroups of 3-manifold groups, giving essentially algebraic arguments that extend to the case of $PD_3$-groups and group pairs. However the argument relies on an $L^2$-Betti number hypothesis…
This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2
This paper has been withdrawn by the author, due to an error in the proof of Theorem 3.8.
This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.
Paper withdrawn. There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the main results of the paper, are not proved.
This paper has been withdrawn due to a error in Theorem 3.1.
This paper was withdrawn by the authors. Lemma 5.1 is wrong.
We introduce the notion of groups of polytope class and show that torsion-free amenable groups satisfying the Atiyah Conjecture possess this property. A direct consequence is the homotopy invariance of the $L^2$-torsion polytope among…
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.