| Every gradient-like flow on a compact metric space determines a topological category whose object are the rest points and morphisms are flow lines of the flow. Cohen, Jones, and Segal proved that if the flow is Morse Smale (with no periodic orbits) on a compact manifold then the classifying space of the corresponding topological category is homoeomorphic to underlying manifold. In the paper we improve the above theorem by proving that the Morse Smale flow is topologically conjugent to a projective flow. The notion of a projective flow is also defined in the paper. |
