Topology of generic foliations on Stein manifolds: structure of leaves   and Kupka-Smale property
  We study topology of leaves of 1-dimensional singular holomorphic foliations of Stein manifolds. We prove that for a generic foliation all leaves, except for at most countably many, are contractible, the rest are topological cylinders. We show that a generic foliation is complex Kupka-Smale. 
Tanya Firsova
math.DS math.CV