几乎为正的联系是强烈的准正联系。

IF 1.3 2区数学 Q1 MATHEMATICS Mathematische Annalen Pub Date : 2023-01-01 DOI:10.1007/s00208-021-02328-x

Peter Feller, Lukas Lewark, Andrew Lobb

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引用次数: 4

摘要

我们证明了含有一个单负交叉的图的任何环节都是强拟正的。这回答了Stoimenow的一个(强烈)肯定的问题。作为第二个主要结果，我们给出了具有拟正正则曲面(由Seifert算法产生的曲面)的连接图的一个简单而完整的表征。作为应用，我们确定了13个交叉点以内的哪些素数结是强拟正的，并且对于具有实现其属的正则曲面的结，我们证实了以下猜想:当且仅当Bennequin不等式是一个等式时，一个结是强拟正的。

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Almost positive links are strongly quasipositive.

We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give a simple and complete characterization of link diagrams with quasipositive canonical surface (the surface produced by Seifert's algorithm). As applications, we determine which prime knots up to 13 crossings are strongly quasipositive, and we confirm the following conjecture for knots that have a canonical surface realizing their genus: a knot is strongly quasipositive if and only if the Bennequin inequality is an equality.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.