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 , we determine that have tunnel number while the remaining all have tunnel number . Notably, these manifolds contain asymmetric L-space knot complements. Furthermore, using SnapPy and KLO we find presentations of these knots as closures of positive braids that realize the Morton-Franks-Williams bound on braid index. The smallest of these has genus and braid index .
Keywords
Cite
@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}
}
Comments
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