## Geometry and Topology

•  Michael Willis, Stanford University
•  Annular Khovanov stable homotopy and sl_2
•  07/29/2022
•  1:00 PM - 2:00 PM
•  C304 Wells Hall
•  Teena Meredith Gerhardt (gerhar18@msu.edu)

The Khovanov complex of a link $L$ in a thickened annulus carries a filtration; the associated graded complex gives rise to the annular Khovanov homology of $L$. Grigsby-Licata-Wehrli show that this annular homology admits an action by the Lie algebra $\mathfrak{sl}_2$. Using the techniques of Lipshitz-Sarkar, one can define a stable homotopy lift of the annular Khovanov homology of $L$. In this talk I will describe (in part) how to lift the $\mathfrak{sl}_2$-action to the stable homotopy category as well, illustrating some features of how one might hope to lift signed maps with cancellations via framed flow categories. This is joint work with Ross Akhmechet and Slava Krushkal.

## Contact

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Michigan State University
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