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Christine Lee, PMA 11.176: Characterizing the Khovanov complex for infinite torus braids.
Tuesday, October 11, 2022, 03:30pm - 04:30pm
The Khovanov homology of torus braids on n strands is a central object in quantum topology. By Rozansky, the direct limit of the complex of infinitely many full twists on n strands recovers the categorified Jones-Wenzl projector, and they feature in conjectures by Gorsky-Oblomkov-Rasmussen-Shende, which relate the Khovanov-Rozansky homology of an algebraic link to the Hilbert scheme of points on its defining complex curve. Despite substantial progress on these conjectures, the differentials of the conjectured forms of the complex remain difficult to determine. In this talk, we discuss recent work, joint with Carmen Caprau, Nicolle Gonzalez, Radmila Sazdanovic, and Melissa Zhang, that allows us to characterize a complex simplified from the Khovanov complex of torus braids on n strands. As an application, we give a formula for the Khovanov homology of torus braids on 3-strands and show that Plamenevskaya's invariant for closed braids with sufficiently large fractional Dehn twist coefficient does not vanish.
Location: PMA 11.176

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