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Khovanov homology and
strong inversions
Artem Kotelskiy, Liam Watson and Claudius Zibrowius |
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Vol. 5 (2022), No. 1, 223–244
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Abstract |
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There is a one-to-one correspondence between strong inversions on knots in the three-sphere and a special class of four-ended tangles. We compute the reduced Khovanov homology of such tangles for all strong inversions on knots with up to 9 crossings, and discuss these computations in the context of earlier work by the second author (Adv. Math. 313 (2017), 915–946). In particular, we provide a counterexample to Conjecture 29 therein, as well as a refinement of and additional evidence for Conjecture 28. |
Keywords
Khovanov homology, strong inversion, tangle, immersed
curves
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Mathematical Subject Classification
Primary: 57K10, 57K18
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Milestones
Received: 3 March 2021
Revised: 18 August 2021
Accepted: 2 September 2021
Published: 27 October 2022
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Authors |
| Artem Kotelskiy | |
| Mathematics Department Stony Brook University Stony Brook, NY United States |
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| Liam Watson | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Claudius Zibrowius | |
| Faculty of Mathematics University of Regensburg Regensburg Germany |
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