Capacities from the Chiu-Tamarkin complex
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910661473206272 |
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| author | Zhang, Bingyu |
| author_facet | Zhang, Bingyu |
| contents | In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a $\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of sheaves. We compute $(c_k)_{k\in\mathbb{N}}$ for convex toric domains, which are the same as the Gutt-Hutchings capacities. Our method also works for the prequantized contact manifold $T^*X\times S^1$. We define a sequence of "contact capacities" $([c]_k)_{k\in\mathbb{N}}$ on the prequantized contact manifold $T^*X\times S^1$, and we compute them for prequantized convex toric domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_05143 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Capacities from the Chiu-Tamarkin complex Zhang, Bingyu Symplectic Geometry 53D35(Primary) In this paper, we construct a sequence $(c_k)_{k\in\mathbb{N}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a $\mathbb{Z}/\ell$-equivariant invariant coming from the microlocal theory of sheaves. We compute $(c_k)_{k\in\mathbb{N}}$ for convex toric domains, which are the same as the Gutt-Hutchings capacities. Our method also works for the prequantized contact manifold $T^*X\times S^1$. We define a sequence of "contact capacities" $([c]_k)_{k\in\mathbb{N}}$ on the prequantized contact manifold $T^*X\times S^1$, and we compute them for prequantized convex toric domains. |
| title | Capacities from the Chiu-Tamarkin complex |
| topic | Symplectic Geometry 53D35(Primary) |
| url | https://arxiv.org/abs/2103.05143 |