A minimality property for knots without Khovanov 2-torsion

Onkar Singh Gujral; Joshua Wang

doi:10.2140/agt.2025.25.4073

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arXiv · 2310.06163

A minimality property for knots without Khovanov 2-torsion

Onkar Singh Gujral·Joshua Wang

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Abstract

A conjecture of Shumakovitch states that every nontrivial knot has 2-torsion in its Khovanov homology. We show that if a knot $K$ has no 2-torsion in its Khovanov homology, then the rank of its reduced Khovanov homology is minimal among all knots obtainable from $K$ 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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Onkar Singh Gujral, Joshua Wang. 2023-09-25. A minimality property for knots without Khovanov 2-torsion. https://doi.org/10.2140/agt.2025.25.4073

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