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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.24382 |
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| _version_ | 1866913118027776000 |
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| author | Choa, Dongwook Hu, Jiawei Lau, Siu-Cheong Li, Yan-Lung Leon |
| author_facet | Choa, Dongwook Hu, Jiawei Lau, Siu-Cheong Li, Yan-Lung Leon |
| contents | We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian Floer cohomology upstairs and Lagrangian Floer cohomology of its quotient. Furthermore, we study the symplectic quotient in the presence of nodal type singularities and prove that the equivariant correspondence gives an isomorphism on cohomologies which was conjectured by Lekili-Segal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors Choa, Dongwook Hu, Jiawei Lau, Siu-Cheong Li, Yan-Lung Leon Symplectic Geometry We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian Floer cohomology upstairs and Lagrangian Floer cohomology of its quotient. Furthermore, we study the symplectic quotient in the presence of nodal type singularities and prove that the equivariant correspondence gives an isomorphism on cohomologies which was conjectured by Lekili-Segal. |
| title | Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2512.24382 |