Round handles and homotopy of nonsingular vector fields
Round handles and homotopy of nonsingular vector fields
Introduction.We consider nonsingular vector fields on compact connected C°° manifolds.The question is: What orbit structures occur in which homotopy classes of nonsingular vector fields?We show that in dimensions 4 and greater, a nonsingular Morse-Smale (NMS) vector field occurs in each homotopy class.Under the additional assumption that the first Betti number …