Two curious strongly invertible L-space knots
Geometric Topology
2026-02-10 v3
Abstract
We present two examples of strongly invertible L-space knots whose surgeries are never the double branched cover of a Khovanov thin link in the 3-sphere. Consequently, these knots provide counterexamples to a conjectural characterization of strongly invertible L-space knots due to Watson. We also discuss other exceptional properties of these two knots, for example, these two L-space knots have formal semigroups that are actual semigroups.
Keywords
Cite
@article{arxiv.2409.09833,
title = {Two curious strongly invertible L-space knots},
author = {Kenneth L. Baker and Marc Kegel and Duncan McCoy},
journal= {arXiv preprint arXiv:2409.09833},
year = {2026}
}
Comments
13 pages, 4 figures, 2 tables; V2: The diagram and the braid word of K1 are corrected. Since we do not use both, all computations and results remain the same. V3: Minor changes and corrections following a referee report, accepted for publication at Adv. Math