Capacities from the Chiu-Tamarkin complex

8 Mar 2021  ·  Bingyu Zhang ·

In this paper, we construct a sequence $(c_k)_{k\in\mathbb{Z}_{\geq 1}}$ of symplectic capacities based on the Chiu-Tamarkin complex $C_{T,\ell}$, a $\mathbb{Z}/\ell\mathbb{Z}$-equivariant invariant coming from the microlocal theory of sheaves. We compute $(c_k)_{k\in\mathbb{Z}_{\geq 1}}$ for convex toric domains, which are the same as the Gutt-Hutchings capacities... On the other hand, our method works for the contact embedding problem. We define a sequence of "contact capacities" $([c]_k)_{k\in\mathbb{Z}_{\geq 1}}$ on the prequantized contact manifold $\mathbb{R}^{2d}\times S^1$, which could derive some embedding obstructions of prequantized convex toric domains. read more

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Symplectic Geometry 53D35(Primary)