A Lagrangian filling for every cluster seed
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909281184382976 |
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| author | Casals, Roger Gao, Honghao |
| author_facet | Casals, Roger Gao, Honghao |
| contents | We show that each cluster seed in the augmentation variety is inhabited by an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings to cluster seeds. The main new technique to produce these Lagrangian fillings is the construction and study of a quiver with potential associated to curve configurations. We prove that its deformation space is trivial and show how to use it to manipulate Lagrangian fillings with $\mathbb{L}$-compressing systems via Lagrangian disk surgeries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00043 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Lagrangian filling for every cluster seed Casals, Roger Gao, Honghao Symplectic Geometry Combinatorics Geometric Topology Representation Theory 53D12, 57K33, 13F60 We show that each cluster seed in the augmentation variety is inhabited by an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian fillings to cluster seeds. The main new technique to produce these Lagrangian fillings is the construction and study of a quiver with potential associated to curve configurations. We prove that its deformation space is trivial and show how to use it to manipulate Lagrangian fillings with $\mathbb{L}$-compressing systems via Lagrangian disk surgeries. |
| title | A Lagrangian filling for every cluster seed |
| topic | Symplectic Geometry Combinatorics Geometric Topology Representation Theory 53D12, 57K33, 13F60 |
| url | https://arxiv.org/abs/2308.00043 |