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arXiv · 2012.08739

Simple Smale flows and their templates on $S^3$

Xiang Liu·Xuezhi Zhao
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Abstract

The embedded template is a geometric tool in dynamics being used to model knots and links as periodic orbits of $3$-dimensional flows. We prove that for an embedded template in $S^3$ with fixed homeomorphism type, its boundary as a trivalent spatial graph is a complete isotopic invariant. Moreover, we construct an invariant of embedded templates by Kauffman's invariant of spatial graphs, which is a set of knots and links. As application, the isotopic classification of simple Smale flows on $S^3$ is discussed.

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Xiang Liu, Xuezhi Zhao. 2020-12-16. Simple Smale flows and their templates on $S^3$. https://doi.org/10.1016/j.topol.2020.107551

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