L-space knots with tunnel number >1 by experiment

Chris Anderson,Kenneth L Baker,Xinghua Gao,Marc Kegel,Khanh Le,Kyle Miller,Sinem Onaran,Geoffrey Sangston,Samuel Tripp,Adam Wood,Ana Wright

doi:10.1080/10586458.2021.1980753

L-space knots with tunnel number >1 by experiment

Chris Anderson, Kenneth L Baker + Show 9 more

https://doi.org/10.1080/10586458.2021.1980753

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Journal: Experimental Mathematics	Publication Date: Sep 30, 2021
Citations: 1

Affiliation: University of California, Berkeley, Humboldt-Universität zu Berlin, Hacettepe University, Temple University, University of Nebraska–Lincoln, University of Melbourne, Dartmouth College, University of Miami, University of Maryland, College Park, University of Illinois Urbana-Champaign

#L-space Knots #Tunnel Number + Show 4 more

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Abstract

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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