On the Geometry of Holomorphic Flows and Foliations Having Transverse Sections

One of the main tools in the study of real foliations of codimension one is the use of transverse sections. Given a codimension one real foliation on a compact manifold there is always a transverse circle and the topology of its embedding into the ambient manifold often has important consequences on the global behavior of the foliation; as in Haefliger’s Theorem and Novikov’s c7ompact leaf theorem for instance.