Related papers: Graphs of groups and the Atiyah conjecture for one…
This paper has been withdrawn by the author due to the gaps in the proofs of Proposition 2.2 and Proposition 3.2
Let G be a torsion free discrete group and let \bar{Q} denote the field of algebraic numbers in C. We prove that \bar{Q}[G] fulfills the Atiyah conjecture if G lies in a certain class of groups D, which contains in particular all groups…
The paper has been withdrawn by the author, due a gap in the proof of Theorem 6.1. The gap was discovered by M. Van den Bergh. Theorem 6.1 is used to prove the main result of the paper, namely Theorem 0.7 (decomposition in arbitrary…
Let $G$ be a regular graph of degree $d$ and let $A\subset V(G)$. Say that $A$ is $\eta$-closed if the average degree of the subgraph induced by $A$ is at least $\eta d$. This says that if we choose a random vertex $x\in A$ and a random…
We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper
The paper is withdrawn by the authors and replaced be an improved and extended version arxiv: 0812.2968
This paper is being withdrawn as its main results are already included in section 2 of the paper hep-lat/9901006.
This paper has been withdrawn by the author due to a serious gap in the proof of the main theorem.
We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these invariants is obtained from the definition of L^2 homology…
An elementary gap in the proof of corollary 2.2 was found, the claim in the first version of the paper is thus retracted.
In topology there is a theorem of Atiyah, concerning K-theory of classifying space of connected compact Lie group. We consider an algebraic analogue of this theorem. We prove that for a split reductive algebraic group G over a field there…
This paper, which commented on Newman and Leicht's "Mixture models and exploratory analysis in networks" (2007, PNAS 104, 9564-9569), has been withdrawn. The reason for this removal is that we misinterpreted the conceptual framework that…
This paper has been withdrawn by the author due to a gap in the proof of the main result.
This paper has been withdrawn by author due to an error in the proof.
The paper is withdrawn due to mistakes in the proofs for Proposition 1.2 and Theorem 2.2.
This paper has been withdrawn by the author(s), due a crucial sign error in Thm. 11.
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
This paper is originally designed as a part of revision of the author's preprint math.AG/9908174 "P-adic Schwarzian triangle groups of Mumford type". Recently, Yves Andr'e pointed out a flaw in that preprint; more precisely, Proposition II…
This paper has been withdrawn by the authors due to essential errors in Theorem 5.6.
We provide a proof for an inequality between volume and L2-Betti numbers of aspherical manifolds for which Gromov outlined a strategy based on general ideas of Connes. The implementation of that strategy involves measured equivalence…