L-space knots with tunnel number >1 by experiment

被引：1

作者：

Anderson, Chris ^{[1
]}

Baker, Kenneth L. ^{[1
]}

Gao, Xinghua ^{[2
]}

Kegel, Marc ^{[3
]}

Le, Khanh ^{[4
]}

Miller, Kyle ^{[5
]}

Onaran, Sinem ^{[6
]}

Sangston, Geoffrey ^{[7
]}

Tripp, Samuel ^{[8
]}

Wood, Adam ^{[9
]}

Wright, Ana ^{[10
]}

机构：

[1] Univ Miami, Dept Math, Coral Gables, FL USA

[2] Univ Illinois, Dept Math, 1409 W Green St, Urbana, IL 61801 USA

[3] Humboldt Univ, Inst Math, Berlin, Germany

[4] Temple Univ, Dept Math, Philadelphia, PA 19122 USA

[5] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[6] Hacettepe Univ, Dept Math, Ankara, Turkey

[7] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[8] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

[9] Univ Melbourne, Dept Math & Stat, Parkville, Vic 3052, Australia

[10] Univ Nebraska, Dept Math, Lincoln, NE USA

来源：

EXPERIMENTAL MATHEMATICS | 2023年 / 32卷 / 04期

基金：

美国国家科学基金会;

关键词：

Braid; L-space knot; asymmetric; SnapPy; FLOER HOMOLOGY; SURGERY;

D O I：

10.1080/10586458.2021.1980753

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：600 / 614

页数：15

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