Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simple Smale flows and their templates on $S^3$   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.

31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess