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Geometry and Topology Seminar

Friday, May 12, 2023
4:00pm to 5:00pm
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Linde Hall 187
An $L_\infty$-module structure on annular Khovanov homology
Champ Davis, Department of Mathematics, University of Oregon,

Khovanov homology is one of the most popular tools used to study links in $S^3$.  If the link is in a thickened annulus, there is an annular refinement of Khovanov homology that contains additional structure.  In particular, Grigsby-Licata-Wehrli showed that the annular Khovanov homology of $L$ is equipped with an action of $sl_2(\wedge)$, the exterior current algebra of the Lie algebra $sl_2$.  We will discuss how this structure can be understood in the setting of $L_\infty$-algebras and modules.  We show that $sl_2(\wedge)$ is an $L_\infty$-algebra and that the annular Khovanov homology of $L$ is an $L_\infty$-module over $sl_2(\wedge)$.  Up to $L_\infty$-quasi-isomorphism, this structure is invariant under Reidemeister moves, and the higher $L_\infty$-operations can be computed using explicit formulas.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit