Holomorphic one-forms, fibrations over the circle, and characteristic numbers of Kähler manifolds

Abstract

AbstractWe prove that the only relation imposed on the Hodge and Chern numbers of a compact Kähler manifold by the existence of a nowhere zero holomorphic one-form is the vanishing of the Hirzebruch genus. We also treat the analogous problem for nowhere zero closed one-forms on smooth manifolds.