L-space knots with tunnel number >1 by experiment


Anderson C., Baker K. L. , Gao X., Kegel M., Le K., Miller K., ...More

EXPERIMENTAL MATHEMATICS, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.1080/10586458.2021.1980753
  • Title of Journal : EXPERIMENTAL MATHEMATICS
  • Keywords: Braid, L-space knot, asymmetric, SnapPy, FLOER HOMOLOGY, SURGERY

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.