The set of vector fields with transverse foliations (Q1309175)

Let \(M\) be a smooth three dimensional closed manifold and \(NSX(M)\) the space of \(C^ 1\) nonsingular vector fields on \(M\), endowed with the \(C^ 0\)-topology. By \(TF(M)\) is denoted the topological subspace of \(NSX(M)\) of vector fields whose flows admit a transverse foliation and by \(\overline{TF(M)}\) its closure. The author introduces the notion of homotopically linked flow. Then \(L(M)\) is the subset of \(NSX(M)\) consisting of vector fields whose flows are homotopically linked. The author proved among others that the sets \(TF(M)\) and \(L(M)\) are open and not dense in \(NSX(M)\), \(TF(M) \subset L(M) \subset \overline{TF(M)}\) and the \(TF(M)\) is invariant under topological conjugacy. This interesting paper is well written and organized.