Topological Fukaya category of tagged arcs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913316570398720 |
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| author | Cho, Cheol-Hyun Kim, Kyoungmo |
| author_facet | Cho, Cheol-Hyun Kim, Kyoungmo |
| contents | A tagged arc on a surface is introduced by Fomin, Shapiro, and Thurston to study cluster theory on marked surfaces. Given a tagged arc system on a graded marked surface, we define its $\mathbb{Z}$-graded $\mathcal{A}_\infty$-category, generalizing the construction of Haiden, Katzarkov, and Kontsevich for arc systems. When a tagged arc system arises from a non-trivial involution on a marked surface, we show that this $\mathcal{A}_\infty$-category is quasi-isomorphic to the invariant part of the topological Fukaya category under the involution. In particular, this identifies tagged arcs with non-geometric idempotents of Fukaya category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10294 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Fukaya category of tagged arcs Cho, Cheol-Hyun Kim, Kyoungmo Symplectic Geometry Rings and Algebras Representation Theory 53D37, 16E35 A tagged arc on a surface is introduced by Fomin, Shapiro, and Thurston to study cluster theory on marked surfaces. Given a tagged arc system on a graded marked surface, we define its $\mathbb{Z}$-graded $\mathcal{A}_\infty$-category, generalizing the construction of Haiden, Katzarkov, and Kontsevich for arc systems. When a tagged arc system arises from a non-trivial involution on a marked surface, we show that this $\mathcal{A}_\infty$-category is quasi-isomorphic to the invariant part of the topological Fukaya category under the involution. In particular, this identifies tagged arcs with non-geometric idempotents of Fukaya category. |
| title | Topological Fukaya category of tagged arcs |
| topic | Symplectic Geometry Rings and Algebras Representation Theory 53D37, 16E35 |
| url | https://arxiv.org/abs/2404.10294 |