Symplectic embeddings of balls into disk 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 such a bundle. The purpose of this paper is to study symplectic embeddings of balls into the associated disk bundles. To this end, we compute the ECH cobordism maps induced by these disk bundles. In addition, we compute the ECH spectrum of the prequantization bundles over the sphere and the torus.