The aim is to understand how one-dimensional basic sets can be embedded in flows on 3-manifolds. The primary model for one-dimensional basic sets is provided by templates (branched 2-manifolds with expansive flow), obtained by collapsing a Markov flowbox neighborhood of the basic set along its stable foliation. We describe an algorithm telling whether a given template can be part of some non-singular Smale flow on the 3-sphere. Additionally, a few quick-check necessary conditions are provided in some specific cases. Most of the methods are relevant to the study of arbitrary three-dimensional manifolds with boundary and tangencies, embedded in flows, not only those originating from basic sets.
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