Vector fields with transverse foliations
In any homotopy class of nonsingular vector fields of any closed oriented n-manifold there is an open set with no transverse foliation. For \(n=3\) this follows from the failure of a linking property which is a necessary condition for the flow to have a transverse foliation. The author shows that for a nonsingular Morse-Smale flow on a closed oriented 3-manifold the linking property is also a sufficient condition.
homotopy class of nonsingular vector fields
nonsingular Morse-Smale flow on a closed oriented 3-manifold
scientific article; zbMATH DE number 3929961