Iltgen, Damian and Lewark, Lukas and Marino, Laura (2025) Khovanov homology and rational unknotting. QUANTUM TOPOLOGY, 16 (4). pp. 655-741. ISSN 1663-487X, 1664-073X
Full text not available from this repository. (Request a copy)Abstract
Building on the work by Alishahi-Dowlin, we extract a new knot invariant ) >= 0 from universal Khovanov homology. While ) is a lower bound for the unknotting number, in fact more is true: ) is a lower bound for the proper rational unknotting number (the minimal number of rational tangle replacements preserving connectivity necessary to relate a knot to the unknot). Moreover, we show that, for all n >= 0, there exists a knot K with )(K) = n. Along the way, following Thompson, we compute the Bar-Natan complexes of rational tangles.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | FLOER HOMOLOGY; LINK HOMOLOGY; NUMBER; COBORDISMS; TORSION; TANGLE; Khovanov homology; Bar-Natan homology; Frobenius algebra; Rasmussen invariant; unknotting number; rational tangles |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 23 Jun 2026 09:35 |
| Last Modified: | 23 Jun 2026 09:35 |
| URI: | https://pred.uni-regensburg.de/id/eprint/66385 |
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