The topology of Lagrangian submanifolds via open-closed string topology
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915927655710720 |
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| author | Li, Shuhao |
| author_facet | Li, Shuhao |
| contents | We study the topology of Lagrangian submanifolds in standard symplectic vector spaces $\mathbb{C}^n$ using ideas from open-closed string topology. Specifically, for a closed, oriented, spin Lagrangian $L$, we construct a (possibly curved) deformation of the dg associative algebra of chains on the based loop space of $L$. This is done via pushing forward moduli spaces of pseudo-holomorphic discs with boundaries on $L$, viewed as chains in the free loop space, along a string topology closed-open map. As an application, we prove that if $π_2(L)=0$, then $L$ has non-vanishing Maslov class, generalizing previous results due to Viterbo, Cieliebak-Mohnke, Fukaya, and Irie. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08481 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The topology of Lagrangian submanifolds via open-closed string topology Li, Shuhao Symplectic Geometry Algebraic Topology General Topology 53D12, 53D40, 55P50 We study the topology of Lagrangian submanifolds in standard symplectic vector spaces $\mathbb{C}^n$ using ideas from open-closed string topology. Specifically, for a closed, oriented, spin Lagrangian $L$, we construct a (possibly curved) deformation of the dg associative algebra of chains on the based loop space of $L$. This is done via pushing forward moduli spaces of pseudo-holomorphic discs with boundaries on $L$, viewed as chains in the free loop space, along a string topology closed-open map. As an application, we prove that if $π_2(L)=0$, then $L$ has non-vanishing Maslov class, generalizing previous results due to Viterbo, Cieliebak-Mohnke, Fukaya, and Irie. |
| title | The topology of Lagrangian submanifolds via open-closed string topology |
| topic | Symplectic Geometry Algebraic Topology General Topology 53D12, 53D40, 55P50 |
| url | https://arxiv.org/abs/2604.08481 |