Year: 2026
Type: preprint
Abstract: We determine $2,540$ unknotting numbers of prime knots with at most $13$ crossings, that are unknown in the KnotInfo snapshot of 9 September 2026. The lower-bound calculations use Heegaard Floer correction-term obstructions and Greene's spanning-tree model. We also give explicit crossing-change constructions for upper bounds. For $959$ alternating knots with range $[2,3]$, we verify that no crossing change in a minimal diagram gives a knot of unknotting number one. We determine the unknotting numbers of all four knots in Brittenham and Hermiller's construction and thereby identify 13n3370 as an explicit counterexample to the original Bernhard-Jablan conjecture.
Source: arXiv (Cornell University)
Author: Lee, Seong-Jin
Institution: Institute for Basic Science
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5387446297, G670587537
OpenAlex ID: W7212136660