Related papers: Graphs of groups and the Atiyah conjecture for one…
This paper has been withdrawn by the author, due to a crucial error in page 5.
When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. The main result that makes this possible is…
The article is withdrawn. Its content is contained in the final version of arXiv:0805.1634.
This paper has been withdrawn by the authors, due an error in Bethe Ansatz equations (16).
In a recent work, Keusch proved the so-called 1-2-3 Conjecture, raised by Karo\'nski, {\L}uczak, and Thomason in 2004: for every connected graph different from $K_2$, we can assign labels~$1,2,3$ to the edges so that no two adjacent…
The present constitutes the key lemma which was hitherto missing in the author's proof of, inter alia, the Green-Griffiths conjecture for surfaces with enough 2-jets, e.g. $13\mathrm{c}_1^2> 9\mathrm{c}_2$. As to why this is so is not the…
This paper was withdrawn by the author. The appearance of an author-written addendum [3] to the paper [2] made our correction note [1] to that paper superfluous and hence it is no longer available here. [1] Dror Bar-Natan and Ofer Ron, A…
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the $n$-ball is simple for $n \ge 3$, asked if the same statement holds in dimension $2$. We show that the group of compactly…
This paper has been withdrawn by the author(s), due the final version in math.QA/0604564
This paper has been withdrawn by the author due to the version of [A complete proof of Hamilton's conjecture] at arXiv:1008.1576
This paper has been withdrawn by the author due to an error in Lemma 3, making the (bijective) proof of Theorem 4 and Corollary 5 invalid (symmetry of k-nonnesting and k-noncrossing set partitions).
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
We show that the class of groups satisfying the K- and L-theoretic Farrell-Jones conjecture is closed under taking graph products of groups.
Let G be a group such that its finite subgroups have bounded order, let d denote the lowest common multiple of the orders of the finite subgroups of G, and let K be a subfield of C that is closed under complex conjugation. Let U(G) denote…
This paper has been withdrawn by the author, due to an error in the proof of lemma 7.4. However, numerical evidence strongly suggest that this lemma is true.
This is an English translation of three articles, originally written in German, by Wilhelm Magnus (1907--1990). The articles are from 1930, 1931, and 1932, respectively, and were the first articles published on one-relator group theory. The…
In this paper, a notion of a principal $2$-bundle over a Lie groupoid has been introduced. For such principal $2$-bundles, we produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures…
For each odd prime p, we exhibit p-groups G of p-rank two such that (suitably defined) Chern classes of unitary representations of G fail to generate the following rings: 1. The even degree integral cohomology of G; 2. The final page of the…
This paper is withdrawn. We found a mistake in Lemma 4.1
This paper is withdrawn due to some gaps in the proof