Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds

Details Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds Regular level sets of Lyapunov graphs of nonsingular Smale flows on 3-manifolds

2010-07-20

arxiv.org/abs/1007.3333v1

Mathematics

Geometric Topology

14 pages, 9 figures

Scientific paper

In this paper, we first discuss the regular level set of a nonsingular Smale flow (NSF) on a 3-manifold. The main result about this topic is that a 3-manifold $M$ admits an NSF flow which has a regular level set homeomorphic to $(n+1)T^{2}$ $(n\in \mathbb{Z}, n\geq 0)$ if and only if $M=M'\sharp n S^{1}\times S^{2}$. Then we discuss how to realize a template as a basic set of an NSF on a 3-manifold. We focus on the connection between the genus of the template $T$ and the topological structure of the realizing 3-manifold $M$.

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