通过实验发现隧道数大于 1 的 L 空间结点

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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