Fat handles and phase portraits of Non Singular Morse-Smale ows on S3 with unknotted saddle orbits.

Abstract

In this paper we build Non-singular Morse-Smale ows on S3 with unknotted and unlinked saddle orbits by identifying fat round handles along their boundaries. This way of building the ows enables to get their phase portraits. We also show that the presence of heteroclinic trajectories imposes an order in the round handle decomposition of these ows; this order is total for NMS ows composed of one repulsive, one attractive and n unknotted saddle orbits, for n > 1