From Lagrangian Products to Toric Domains via the Toda Lattice
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915367034552320 |
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| author | Ostrover, Yaron Ramos, Vinicius G. B. Sepe, Daniele |
| author_facet | Ostrover, Yaron Ramos, Vinicius G. B. Sepe, Daniele |
| contents | In this paper we use the periodic Toda lattice to show that certain Lagrangian product configurations in the classical phase space are symplectically equivalent to toric domains. In particular, we prove that the Lagrangian product of a certain simplex and the Voronoi cell of the root lattice $A_n$ is symplectically equivalent to a Euclidean ball. As a consequence, we deduce that the Lagrangian product of an equilateral triangle and a regular hexagon is symplectomorphic to a Euclidean ball in dimension 4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10912 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | From Lagrangian Products to Toric Domains via the Toda Lattice Ostrover, Yaron Ramos, Vinicius G. B. Sepe, Daniele Symplectic Geometry Dynamical Systems In this paper we use the periodic Toda lattice to show that certain Lagrangian product configurations in the classical phase space are symplectically equivalent to toric domains. In particular, we prove that the Lagrangian product of a certain simplex and the Voronoi cell of the root lattice $A_n$ is symplectically equivalent to a Euclidean ball. As a consequence, we deduce that the Lagrangian product of an equilateral triangle and a regular hexagon is symplectomorphic to a Euclidean ball in dimension 4. |
| title | From Lagrangian Products to Toric Domains via the Toda Lattice |
| topic | Symplectic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2309.10912 |