Abstract
This chapter discusses foliations transverse to nonsingular Morse–Smale flows and describes codimension one foliations on S3 transverse to a nonsingular Morse–Smale flow. In general, nonsingular Morse–Smale flows do not admit codimension one transverse foliations. The chapter presents the characterization of the nonsingular Morse–Smale flows with transverse foliations. A nonsingular Morse–Smale flow admits a codimension one transverse foliation only if the flow is essential or the flow has the linking property. If a manifold is divided into two or more pieces by compact leaves, then there are no relations between foliations on each piece. A nonsingular Morse–Smale flow on a manifold M is a flow that satisfies the condition that there are no singular points, and the nonwandering set consists of a finite number of closed orbits.
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