Periodic prime knots and topologically transitive flows on 3-manifolds
Given a smooth nonsingular topologically transitive flow on a closed 3-manifold with integer homology zero in dimension 2, then by the main result there is an open dense subset such that any closed orbit intersecting the subset is a nontrivial prime knot. Here, in transferring notions from classical knot theory, a knot is trivial if it bounds a disk, a knot is composite if it meets a 2-sphere in two points that reduce the knot to two nontrivial ones, and a knot is prime if it is nontrivial but not composite. The above result is deduced from work of the first author [Topology Appl. 135, 131--148 (2004; Zbl 1032.37007), and Topology 43, 697--703 (2004; Zbl 1079.57002)] as well as a technical method involving foliations by \textit{C. Gutierrez} [Topology 34, 679--698 (1995; Zbl 0842.57032)].
scientific article; zbMATH DE number 5013536
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