Exact Lagrangian fillings of twist-spun torus links
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916964664868864 |
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| author | Chen, Vincent Galloway, Patton Hughes, James Wei, Luciana |
| author_facet | Chen, Vincent Galloway, Patton Hughes, James Wei, Luciana |
| contents | We construct exact Lagrangian fillings of Legendrian torus links $Λ(k, n-k)$ that are fixed by a Legendrian loop that acts by $2π\ell/n$ rotation. Using these rotationally symmetric fillings, we produce fillings of the corresponding Legendrian twist-spun tori. Our construction is combinatorial in nature, relating symmetric weakly separated collections and plabic graphs to symmetric Legendrian weaves via the T-shift procedure of Casals, Le, Sherman-Bennett, and Weng. The main technical ingredient in this process is a necessary and sufficient condition for the existence of maximal weakly separated collections of $k$-element subsets of $\{1, \dots, n\}$ that are fixed by addition of $\ell$ modulo $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19095 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact Lagrangian fillings of twist-spun torus links Chen, Vincent Galloway, Patton Hughes, James Wei, Luciana Symplectic Geometry Combinatorics 53D12, 53D35, 13F60 We construct exact Lagrangian fillings of Legendrian torus links $Λ(k, n-k)$ that are fixed by a Legendrian loop that acts by $2π\ell/n$ rotation. Using these rotationally symmetric fillings, we produce fillings of the corresponding Legendrian twist-spun tori. Our construction is combinatorial in nature, relating symmetric weakly separated collections and plabic graphs to symmetric Legendrian weaves via the T-shift procedure of Casals, Le, Sherman-Bennett, and Weng. The main technical ingredient in this process is a necessary and sufficient condition for the existence of maximal weakly separated collections of $k$-element subsets of $\{1, \dots, n\}$ that are fixed by addition of $\ell$ modulo $n$. |
| title | Exact Lagrangian fillings of twist-spun torus links |
| topic | Symplectic Geometry Combinatorics 53D12, 53D35, 13F60 |
| url | https://arxiv.org/abs/2509.19095 |