实验得到的隧道数大于 1 的 L 空间纽结
几何拓扑
2026-02-10 v2
摘要
在 Dunfield 的 SnapPy 普查中双曲流形目录里（这些流形是 S^3 中 L 空间纽结的补空间），我们确定其中有 22 个具有隧道数 2，而其余全部具有隧道数 1。值得注意的是，这 22 个流形包含 9 个非对称 L 空间纽结补空间。此外，利用 SnapPy 与 KLO，我们找到了这 22 个纽结作为正辫子闭包的表述，其实现了辫指数上的 Morton-Franks-Williams 界。其中最小者具有亏格 12 与辫指数 4。
引用
@article{arxiv.1909.00790,
title = {L-space knots with tunnel number >1 by experiment},
author = {Chris Anderson and Kenneth L. Baker and Xinghua Gao and Marc Kegel and Khanh Le and Kyle Miller and Sinem Onaran and Geoffrey Sangston and Samuel Tripp and Adam Wood and Ana Wright},
journal= {arXiv preprint arXiv:1909.00790},
year = {2026}
}
备注
This is a significant expansion/rewrite of the original version. The title and abstract have both changed to reflect this. Relevant code is included in the body of the article itself. Originally, this was a note that collected the results of an "office hour" session on the use of SnapPy and KLO held at the ICERM workshop Perspectives on Dehn Surgery, July 15--19, 2019