A local $\mathfrak{gl}_{1|1}$-action on odd Khovanov homology
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911246633140224 |
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| author | Ebert, Mark Schelstraete, Léo |
| author_facet | Ebert, Mark Schelstraete, Léo |
| contents | We show that odd Khovanov homology carries an action of the super Lie algebra $\mathfrak{gl}_{1|1}$, given extra choice of markings on the link. Moreover, we show that this action arises from an action on super $\mathfrak{gl}_{2}$-foams, in the extended-TQFT framework developed by the second author and Vaz; in particular, it extends to tangles. Finally, we relate the action to torsion $\mathbb{Z}/n\mathbb{Z}$ in pretzel links $P(n,n,-n)$. In particular, this shows that all torsion can appear in odd Khovanov homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A local $\mathfrak{gl}_{1|1}$-action on odd Khovanov homology Ebert, Mark Schelstraete, Léo Geometric Topology Representation Theory 57K18, 18N25, 17B37 We show that odd Khovanov homology carries an action of the super Lie algebra $\mathfrak{gl}_{1|1}$, given extra choice of markings on the link. Moreover, we show that this action arises from an action on super $\mathfrak{gl}_{2}$-foams, in the extended-TQFT framework developed by the second author and Vaz; in particular, it extends to tangles. Finally, we relate the action to torsion $\mathbb{Z}/n\mathbb{Z}$ in pretzel links $P(n,n,-n)$. In particular, this shows that all torsion can appear in odd Khovanov homology. |
| title | A local $\mathfrak{gl}_{1|1}$-action on odd Khovanov homology |
| topic | Geometric Topology Representation Theory 57K18, 18N25, 17B37 |
| url | https://arxiv.org/abs/2511.00947 |