Stable Khovanov homology of torus links and volume
Moduli and Friends seminar
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Monday 29 May 2023

Christine Ruey Shan Lee (Texas State University)Stable Khovanov homology of torus links and volume

Let T(n,k) denote the (n,k)-torus braid. It is well known that the Jones polynomial and the Khovanov homology of torus links stabilize as k → ∞ by the work of Champanekar-Kofman and Stosic. In particular, Rozanksy showed that the stable Khovanov homology of torus links exists as the direct limit of the Khovanov homology of T(n,k)-torus links, and the stable Khovanov homology recovers the categorification of the Jones-Wenzl projector. We show that Khovanov homology of a link stabilizes under twisting as a categorial analogue of the result by Champanekar-Kofman, extending the results by Stosic and Rozansky. Since the Jones-Wenzl projector can be used to define the colored Jones polynomial, we will discuss a relationship between this stable Khovanov homology to the hyperbolic volume in the spirit of the volume conjecture.

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