The templates of non-singular Smale flows on three manifolds

Abstract

AbstractIn this paper, we first discuss some connections between template theory and the description of basic sets of Smale flows on 3-manifolds due to F. Béguin and C. Bonatti. The main tools we use are symbolic dynamics, template moves and some combinatorial surgeries. Secondly, we obtain some relationship between the surgeries and the number of S1×S2 factors of M for a non-singular Smale flow on a given closed orientable 3-manifold M. We also prove that any template T can model a basic set Λ of a non-singular Smale flow on nS1×S2 for some positive integer n.