Orbifold Floer spectral invariants, symmetric product links and Weyl laws
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866914207893553152 |
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| author | Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan |
| author_facet | Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan |
| contents | We explain a strategy, based on spectral invariants on symmetric product orbifolds, for proving the smooth closing lemma for Hamiltonian diffeomorphisms of a symplectic manifold when the orbifold quantum cohomologies of its symmetric products possess suitable idempotents. We relate the existence of such idempotents to the manifold containing a sequence of Lagrangian links, whose number of components tends to infinity, satisfying a number of properties. Orbifold Floer cohomology for global quotient orbifolds is used axiomatically, and is constructed in a companion paper. We illustrate this strategy by giving a new proof of the smooth closing lemma for area-preserving diffeomorphisms of the 2-sphere. The construction of suitable Lagrangian links in higher dimensions remains an intriguing open problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_00454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orbifold Floer spectral invariants, symmetric product links and Weyl laws Mak, Cheuk Yu Seyfaddini, Sobhan Smith, Ivan Symplectic Geometry We explain a strategy, based on spectral invariants on symmetric product orbifolds, for proving the smooth closing lemma for Hamiltonian diffeomorphisms of a symplectic manifold when the orbifold quantum cohomologies of its symmetric products possess suitable idempotents. We relate the existence of such idempotents to the manifold containing a sequence of Lagrangian links, whose number of components tends to infinity, satisfying a number of properties. Orbifold Floer cohomology for global quotient orbifolds is used axiomatically, and is constructed in a companion paper. We illustrate this strategy by giving a new proof of the smooth closing lemma for area-preserving diffeomorphisms of the 2-sphere. The construction of suitable Lagrangian links in higher dimensions remains an intriguing open problem. |
| title | Orbifold Floer spectral invariants, symmetric product links and Weyl laws |
| topic | Symplectic Geometry |
| url | https://arxiv.org/abs/2512.00454 |