Symplectic embeddings of toric domains with boundary a lens space
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arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911188077510656 |
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| author | Trejos, Jonathan |
| author_facet | Trejos, Jonathan |
| contents | We give a combinatorial description of the embedded contact complex (ECC) of a certain family of contact toric lens spaces that we call concave lens spaces. We also define a notion of a concave toric domain that generalizes the usual concave toric domain in a way that possesses a singularity point and has a boundary a lens space. After desingularization these toric domains include the unitary cotangent bundle of $\mathbb{S}^2$ and the unitary cotangent bundle of $\mathbb{R}P^2$. We use the combinatorial expression of the ECC to compute the ECH capacities of these toric domains. Furthermore, for certain concave toric domains we describe a packing of symplectic manifolds that recovers their ECH capacities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_15374 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symplectic embeddings of toric domains with boundary a lens space Trejos, Jonathan Symplectic Geometry Differential Geometry We give a combinatorial description of the embedded contact complex (ECC) of a certain family of contact toric lens spaces that we call concave lens spaces. We also define a notion of a concave toric domain that generalizes the usual concave toric domain in a way that possesses a singularity point and has a boundary a lens space. After desingularization these toric domains include the unitary cotangent bundle of $\mathbb{S}^2$ and the unitary cotangent bundle of $\mathbb{R}P^2$. We use the combinatorial expression of the ECC to compute the ECH capacities of these toric domains. Furthermore, for certain concave toric domains we describe a packing of symplectic manifolds that recovers their ECH capacities. |
| title | Symplectic embeddings of toric domains with boundary a lens space |
| topic | Symplectic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2312.15374 |