Koszul duality and the link surgery formula
Fuente:
arXiv
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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911054118780928 |
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| author | Zemke, Ian |
| author_facet | Zemke, Ian |
| contents | In previous works, the author described an associative algebra whose $A_\infty$-module categories encode the Heegaard Floer Dehn surgery formulas. In this article, we describe the Koszul dual of this algebra. We construct dualizing bimodules, and prove several equivalences of categories. The constructions of this paper have applications to computational problems involving the link surgery formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09964 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Koszul duality and the link surgery formula Zemke, Ian Geometric Topology Rings and Algebras 57K18 (Primary), 57K16 (Secondary) In previous works, the author described an associative algebra whose $A_\infty$-module categories encode the Heegaard Floer Dehn surgery formulas. In this article, we describe the Koszul dual of this algebra. We construct dualizing bimodules, and prove several equivalences of categories. The constructions of this paper have applications to computational problems involving the link surgery formula. |
| title | Koszul duality and the link surgery formula |
| topic | Geometric Topology Rings and Algebras 57K18 (Primary), 57K16 (Secondary) |
| url | https://arxiv.org/abs/2507.09964 |