Two curious strongly invertible L-space knots
arXiv:2409.09833 · doi:10.1016/j.aim.2025.110287
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.
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