通过实验发现隧道数大于 1 的 L 空间结点

IF 0.7 4区数学 Q2 MATHEMATICS

Experimental Mathematics Pub Date : 2023-10-02 DOI:10.1080/10586458.2021.1980753

Chris Anderson, Kenneth L. Baker, Xinghua Gao, Marc Kegel, Khanh Le, Kyle Miller, Sinem Onaran, Geoffrey Sangston, Samuel Tripp, Adam Wood, Ana Wright

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引用次数: 0

摘要

摘要在邓菲尔德（Dunfield）的 SnapPy 普查双曲流形目录（SnapPy 普查中的双曲流形是 S 中 L 空间结的补集）中，我们确定有 22 个流形的隧道编号为 2，而其余所有流形的隧道编号均为 1。值得注意的是，这 22 个流形包含 9 个非对称 L 空间结补集。此外，利用 SnapPy 和 KLO，我们还找到了这 22 个结的正辫状闭包，实现了辫状指数的莫顿-弗兰克斯-威廉姆斯约束。其中最小的绳结属数为 12，辫状指数为 4。

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L-space knots with tunnel number >1 by experiment

ABSTRACT In Dunfield’s catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in S, we determine that 22 have tunnel number 2 while the remaining all have tunnel number 1. Notably, these 22 manifolds contain 9 asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these 22 knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus 12 and braid index 4.

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来源期刊

Experimental Mathematics 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses. Experiment has always been, and increasingly is, an important method of mathematical discovery. (Gauss declared that his way of arriving at mathematical truths was "through systematic experimentation.") Yet this tends to be concealed by the tradition of presenting only elegant, fully developed, and rigorous results. Experimental Mathematics was founded in the belief that theory and experiment feed on each other, and that the mathematical community stands to benefit from a more complete exposure to the experimental process. The early sharing of insights increases the possibility that they will lead to theorems: An interesting conjecture is often formulated by a researcher who lacks the techniques to formalize a proof, while those who have the techniques at their fingertips have been looking elsewhere. Even when the person who had the initial insight goes on to find a proof, a discussion of the heuristic process can be of help, or at least of interest, to other researchers. There is value not only in the discovery itself, but also in the road that leads to it.