ECH spectrum of some prequantization bundles

Abstract

A prequantization bundle is a circle bundle over a symplectic surface with negative Euler class. A connection 1-form induces a natural contact form on it. The purpose of this note is to compute the ECH spectrum of the prequantization bundles of the sphere and the torus. Our proof relies on computations of the ECH cobordism maps induced by the associated line bundles. Using the cobordism maps and some computations on the U maps, we also show that the Gromov width of the unit disk subbundles is bounded by 1.