相关论文: Counterexamples to a conjecture of Woods

The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…

The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize…

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the counterexample to Mordell's Pellian Equation Conjecture that can…

Nous rappelons l'historique de la demonstration de la conjecture des fibres de Seifert, ainsi que ses motivations et ses diverses generalisations. ----- We recall the history of the proof of the Seibert fiber space conjecture, as well as…

In this paper we disprove three conjectures from [M. Dehmer, F. Emmert-Streib, Y. Shi, Interrelations of graph distance measures based on topological indices, PLoS ONE 9 (2014) e94985] on graph distance measures based on topological indices…

This paper has been withdrawn by the authors due to crucial error in the main proof (located in Section 2.4). The authors apologize for any inconveniences.

We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example of a non-Banach Frechet algebra with two inequivalent…

This paper has been withdrawn by the author.

We construct a simple acyclic directed graph for which the Bunkbed Conjecture is false, thereby resolving conjectures posed by Leander and by Hollom.

We give a new proof of some cases of the Baum-Connes conjecture along the lines of a proof of the Farrell-Jones conjecture.

We first propose what we call the Gaussian Moments Conjecture. We then show that the Jacobian Conjecture follows from the Gaussian Moments Conjecture. We also give a counter-example to a more general statement known as the Moments Vanishing…

We prove a variation of Gronwall's lemma.

We show that if there exists a counter example for the rational case of the Franks-Misiurewicz conjecture, then it must exhibit unbounded deviations in the complementary direction of its rotation set.

We give a simple proof of a recent result by J. Schleischitz dealing with a counterexample to the uniform Littlewood conjecture. Our construction is based on simple properties of Fibonacci numbers.

Let $p$ be a fixed prime number, and $N$ be a large integer. The 'Inverse Conjecture for the Gowers norm' states that if the "$d$-th Gowers norm" of a function $f:\F_p^N \to \F_p$ is non-negligible, that is larger than a constant…

The following conjecture was proposed in 2010 by S. Lando. Let M and N be two unions of the same number of disjoint circles in a sphere. Then there exist two spheres in 3-space whose intersection is transversal and is a union of disjoint…

This is an appendix to our paper "An update of the Hirsch Conjecture" (arXiv:0907.1186), containing proofs of some of the results and comments that were omitted in it.

We show that a problem by Yau can not be true in general. The counterexamples are constructed based on the recent work of Wu and Zheng.

We prove the validity of the strong version of the union of uniform closed balls conjecture, formulated in 2011 as [4, Conjecture 2.5], in the plane.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.