Department of Mathematics Calendar
Christine Ruey Shan Lee, Plamenevskaya’s invariant from the stable Khovanov homology of twisted torus knots
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A transverse link is a link in the 3-sphere that is everywhere transverse to the standard contact structure. Transverse links are considered up to transverse isotopy, with classical invariants such as the self-linking number and regular isotopy class. One of the first connections between transverse links and quantum invariants was made by Plamenevskaya in 2006, when she defined a invariant of transverse links from Khovanov homology. Since then, the relationship between this fascinating invariant and contact geometry remains of intense interest. In this talk, I will discuss open questions relating Plamenevskaya’s invariant to the contact-geometric properties of braids such as the Fractional Dehn Twist Coefficient, and how the result, joint with Diana Hubbard, that Plamenevskaya’s invariant stabilizes for twist torus links, may be applied to study these questions.