Capacities from the Chiu-Tamarkin complex

TL;DR

This paper introduces a new sequence of symplectic capacities derived from the Chiu-Tamarkin complex, computes them for convex toric domains, and extends the method to prequantized contact manifolds, linking to existing capacities.

Contribution

It constructs symplectic capacities from the Chiu-Tamarkin complex and computes them explicitly for convex toric domains, also extending to prequantized contact manifolds.

Findings

Capacities match Gutt-Hutchings capacities for convex toric domains.

Method applies to prequantized contact manifolds.

Explicit computations for convex toric domains.

Abstract

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.