在结补和连杆补中的封闭不可压缩子午不可压缩表面上

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2022-09-30 DOI:10.1142/s0218216522500705

Wei Lin

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引用次数: 0

摘要

本文给出了在结补或环补中检测(可能是穿刺的)子向闭合不可压缩曲面的必要条件。这个条件为我们提供了一种方法，可以根据链接图确定任意链接是分裂的还是非分裂的。我们还证明了，直到同位素，在非分裂素数几乎交替的键补中只存在有限多个这样的曲面。最后，通过手工证明某些结是小结的初等证明，证明了必要条件的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On closed incompressible meridionally incompressible surfaces in knot and link complements

In this paper, we give a necessary condition for detecting (possibly punctured) closed incompressible meridionally incompressible surfaces in knot or link complements. This condition provides us a method to determine whether an arbitrary link is split or non-split based on the link diagram. We also prove that, up to isotopy, there only exist finitely many such surfaces in non-split prime almost alternating link complements. Finally, we demonstrate an application of the necessary condition by showing elementary by-hand proofs that some certain knots are small knots.

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来源期刊

Journal of Knot Theory and Its Ramifications 数学-数学

CiteScore

0.80

自引率

40.00%

发文量

127

审稿时长

4-8 weeks

期刊介绍： This Journal is intended as a forum for new developments in knot theory, particularly developments that create connections between knot theory and other aspects of mathematics and natural science. Our stance is interdisciplinary due to the nature of the subject. Knot theory as a core mathematical discipline is subject to many forms of generalization (virtual knots and links, higher-dimensional knots, knots and links in other manifolds, non-spherical knots, recursive systems analogous to knotting). Knots live in a wider mathematical framework (classification of three and higher dimensional manifolds, statistical mechanics and quantum theory, quantum groups, combinatorics of Gauss codes, combinatorics, algorithms and computational complexity, category theory and categorification of topological and algebraic structures, algebraic topology, topological quantum field theories). Papers that will be published include: -new research in the theory of knots and links, and their applications; -new research in related fields; -tutorial and review papers. With this Journal, we hope to serve well researchers in knot theory and related areas of topology, researchers using knot theory in their work, and scientists interested in becoming informed about current work in the theory of knots and its ramifications.