The homotopy class of non-singular Morse-Smale vector fields on 3- manifolds (Q1091005)

Let M be a 3-manifold with Euler characteristic zero. Denote by F(M) the set of homotopy classes of nonsingular vector fields on M. The author studies the problem of the existence of non-singular Morse Smale (NMS) flows in a given homotopy class. For M being a graph manifold prime to \(S^ 1\times S^ 2\) necessary and sufficient conditions are given under which a class \(\Phi\in F(M)\) contains an NMS flow (theorem 1). An analogous result is obtained for a non-graph manifold M supposing M admits an NMS flow (theorem 2).