Realizing full \(n\)-shifts in simple Smale flows (Q505375)

By definition, a nonsingular Smale flow on a \(3\)-manifold has a hyperbolic chain recurrent set with transverse stable and unstable manifolds such that the recurrent set is \(1\)-dimensional. A simple Smale flow is a nonsingular one with three basic sets: an attracting and a repelling closed orbit and a nontrivial saddle. It is known that the saddle set can be realized as the suspension of the full \(n\)-shift. In this work, various link types of the attractor-repeller pair are constructed where the saddle set is a suspension of a full \(n\)-shift. The examples realize unlinked unknots, a Hopf link, a trefoil or a figure-8 knot and meridian, a braid word \(\sigma^{2p+1}\) plus braid axis, and a \((p,3)\)-torus knot plus its unknotted core. The construction repeatedly applies so-called \(\alpha\)-moves to a trivial part of a template.