A minimality property for knots without Khovanov 2-torsion
Geometric Topology
2025-11-05 v1 Quantum Algebra
Abstract
A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from by a proper rational tangle replacement. It follows, for example, that unknotting number 1 knots have 2-torsion in their Khovanov homology.
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Cite
@article{arxiv.2310.06163,
title = {A minimality property for knots without Khovanov 2-torsion},
author = {Onkar Singh Gujral and Joshua Wang},
journal= {arXiv preprint arXiv:2310.06163},
year = {2025}
}
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3 pages