Packing Lagrangian tori
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866914932397703168 |
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| author | Hind, Richard K. Kerman, Ely |
| author_facet | Hind, Richard K. Kerman, Ely |
| contents | In this paper we consider the problem of packing a symplectic manifold with integral Lagrangian tori, that is Lagrangian tori whose area homomorphsims take only integer values. We prove that the Clifford torus in $S^2 \times S^2$ is a maximal integral packing, in the sense that any other integral Lagranian torus must intersect it. In the other direction, we show that in any symplectic polydisk $P(a,b)$ with $a,b>2$, there is at least one integral Lagrangian torus in the complement of the collection of standard product integral Lagrangian tori. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_01772 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Packing Lagrangian tori Hind, Richard K. Kerman, Ely Symplectic Geometry 53D12 In this paper we consider the problem of packing a symplectic manifold with integral Lagrangian tori, that is Lagrangian tori whose area homomorphsims take only integer values. We prove that the Clifford torus in $S^2 \times S^2$ is a maximal integral packing, in the sense that any other integral Lagranian torus must intersect it. In the other direction, we show that in any symplectic polydisk $P(a,b)$ with $a,b>2$, there is at least one integral Lagrangian torus in the complement of the collection of standard product integral Lagrangian tori. |
| title | Packing Lagrangian tori |
| topic | Symplectic Geometry 53D12 |
| url | https://arxiv.org/abs/2109.01772 |