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arXiv · 2501.11547

On the Khovanov homology of 3-braids

Dirk Schuetz
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Abstract

We prove the conjecture of Przytycki and Sazdanovic that the Khovanov homology of the closure of a 3-stranded braid only contains torsion of order 2. This conjecture has been known for six out of seven classes in the Murasugi-classification of 3-braids and we show it for the remaining class. Our proof also works for the other classes and relies on Bar-Natan's version of Khovanov homology for tangles as well as his delooping and cancellation techniques, and the reduced integral Bar-Natan--Lee--Turner spectral sequence. We also show that the Knight-move conjecture holds for 3-braids.

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Dirk Schuetz. 2025-10-03. On the Khovanov homology of 3-braids. https://arxiv.org/abs/2501.11547

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