Related papers: Another proof of M. Kontsevich formality theorem

It is believed arXiv:0808.2762, arXiv:math/9904055 that, among the coefficients entering Kontsevich's formality quasi-isomorphism arXiv:q-alg/9709040, there are irrational (possibly even transcendental) numbers. In this paper, we prove that…

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.

We prove a stronger version of a termination theorem appeared in the paper "On existence of log minimal models II". We essentially just get rid of the redundant assumptions so the proof is almost the same as in there. However, we give a…

We present in this work a new and simple proof of the false centre theorem.

The primary aim of this essay, drawn from the author's MMath dissertation at Oxford, is to present and explain Kontsevich's formality theorem. The first two sections introduce the main topic. Sections 3 and 4 discuss Hochschild…

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

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 article provides a counterexample to a conjecture by Blocki-Zwonek.

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.

We prove a stronger version of the Kontsevich Formality Theorem for orientable manifolds, relating the Batalin-Vilkovisky (BV) algebra of multivector fields and the homotopy BV algebra of multidifferential operators of the manifold.

This article contains the proof of a theorem on orthogonal-Pin duality that was cited without proof in a previous article in this journal.

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…

This paper corrects an error in the authors' earlier work, by proving stronger forms of the basic lemmas

We prove that the construction of our previous paper math.QA/0103190 yields an invariant of tangle cobordisms.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

This paper has been withdrawn by the author.

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…