用有限商判别某些属一结

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Knot Theory and Its Ramifications Pub Date : 2022-10-28 DOI:10.1142/s0218216523500359

Tamunonye Cheetham-West

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引用次数: 2

摘要

利用$\pi_1（S^3\setminus-K）$的有限商，给出了区分$S^3$中的素结$K$与$S^3$中的每个其它结的一个判据。利用Baldwin-Sivek最近的工作，我们将该准则应用于双曲结$5_2$、$15n_{43522}$和每整数$n$的三股椒盐卷饼结$P（-3,3,2n+1）$。

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Distinguishing Some Genus One Knots Using Finite Quotients

We give a criterion for distinguishing a prime knot $K$ in $S^3$ from every other knot in $S^3$ using the finite quotients of $\pi_1(S^3\setminus K)$. Using recent work of Baldwin-Sivek, we apply this criterion to the hyperbolic knots $5_2$, $15n_{43522}$, and the three-strand pretzel knots $P(-3,3,2n+1)$ for every integer $n$.

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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.