Monodromic model for Khovanov–Rozansky homology
<jats:title>Abstract</jats:title> <jats:p>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 individu...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Walter de Gruyter GmbH
2022
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| Online Access: | https://hdl.handle.net/1721.1/145612 |
| _version_ | 1811098138661879808 |
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| author | Bezrukavnikov, Roman Tolmachov, Kostiantyn |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Bezrukavnikov, Roman Tolmachov, Kostiantyn |
| author_sort | Bezrukavnikov, Roman |
| collection | MIT |
| description | <jats:title>Abstract</jats:title>
<jats:p>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.</jats:p> |
| first_indexed | 2024-09-23T17:10:29Z |
| format | Article |
| id | mit-1721.1/145612 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T17:10:29Z |
| publishDate | 2022 |
| publisher | Walter de Gruyter GmbH |
| record_format | dspace |
| spelling | mit-1721.1/1456122023-04-02T03:56:00Z Monodromic model for Khovanov–Rozansky homology Bezrukavnikov, Roman Tolmachov, Kostiantyn Massachusetts Institute of Technology. Department of Mathematics <jats:title>Abstract</jats:title> <jats:p>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.</jats:p> 2022-09-28T18:27:02Z 2022-09-28T18:27:02Z 2022 2022-09-28T18:22:49Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/145612 Bezrukavnikov, Roman and Tolmachov, Kostiantyn. 2022. "Monodromic model for Khovanov–Rozansky homology." Journal für die reine und angewandte Mathematik (Crelles Journal), 2022 (787). en 10.1515/CRELLE-2022-0008 Journal für die reine und angewandte Mathematik (Crelles Journal) Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Walter de Gruyter GmbH De Gruyter |
| spellingShingle | Bezrukavnikov, Roman Tolmachov, Kostiantyn Monodromic model for Khovanov–Rozansky homology |
| title | Monodromic model for Khovanov–Rozansky homology |
| title_full | Monodromic model for Khovanov–Rozansky homology |
| title_fullStr | Monodromic model for Khovanov–Rozansky homology |
| title_full_unstemmed | Monodromic model for Khovanov–Rozansky homology |
| title_short | Monodromic model for Khovanov–Rozansky homology |
| title_sort | monodromic model for khovanov rozansky homology |
| url | https://hdl.handle.net/1721.1/145612 |
| work_keys_str_mv | AT bezrukavnikovroman monodromicmodelforkhovanovrozanskyhomology AT tolmachovkostiantyn monodromicmodelforkhovanovrozanskyhomology |