Monodromic model for Khovanov–Rozansky homology
Name
10.1515_crelle-2022-0008.pdf
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Published version
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566.61 KB
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Author(s)
Bezrukavnikov, Roman
Tolmachov, Kostiantyn
Date Issued
2022
Journal
Journal für die reine und angewandte Mathematik (Crelles Journal)
Publisher
Walter de Gruyter GmbH
Citation
Bezrukavnikov, Roman and Tolmachov, Kostiantyn. 2022. "Monodromic model for Khovanov–Rozansky homology." Journal für die reine und angewandte Mathematik (Crelles Journal), 2022 (787).
Version
Final published version
Abstract
Abstract
We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild cohomology groups (for the zero and the top degree cohomology this reduces to an earlier result of Gorsky, Hogancamp, Mellit and Nakagane). These objects turn out to be closely related to explicit character sheaves corresponding to exterior powers of the reflection representation of the Weyl group. Applying the described functors to the images of braids in the Hecke category of type A we obtain a geometric description for Khovanov–Rozansky knot homology, essentially different from the one considered earlier by Webster and Williamson.
We describe a new geometric model for the Hochschild cohomology of Soergel bimodules based on the monodromic Hecke category studied earlier by the first author and Yun. Moreover, we identify the objects representing individual Hochschild cohomology groups (for the zero and the top degree cohomology this reduces to an earlier result of Gorsky, Hogancamp, Mellit and Nakagane). These objects turn out to be closely related to explicit character sheaves corresponding to exterior powers of the reflection representation of the Weyl group. Applying the described functors to the images of braids in the Hecke category of type A we obtain a geometric description for Khovanov–Rozansky knot homology, essentially different from the one considered earlier by Webster and Williamson.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1515/CRELLE-2022-0008
