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Closed Braids and Torsion in Khovanov Homology Open Access

In 1984, knot theory was revolutionized with the discovery of the Jones polynomial. Fifteen years later, with several questions about it still unanswered, the polynomial was categorified into what is presently known as Khovanov homology. Parts of the Przytycki-Sazdanovic braid conjecture state that the order of the torsion subgroups in the Khovanov homology of a closed braid is less or equal to its braid index. With the discovery of links with large torsion subgroups of even order in their Khovanov homology, this statement has been partially resolved. In this talk, I will resolve the aforementioned statement completely. Finally, I will introduce the first known examples of knots and links containing large odd torsion in their Khovanov homology.

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