Knots and topologically transitive flows on 3-manifolds

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Title: Knots and topologically transitive flows on 3-manifolds
Author: Basener, William
Abstract: Suppose that () is a nonsingular (fixed point free) flow on a smooth three-dimensional manifold M. Suppose the orbit though a point p ∈M is dense in M. Let D be an imbedded disk in M containing p which is transverse to the flow. Suppose that q ∈D is a point in the forward orbit of p. Under certain assumptions on M, which include the case M = S^3, we prove that if q is sufficiently close to p then the orbit segment from p to q together with a compact segment in D from p to q forms a nontrivial prime knot in M (Refer to PDF file for exact formulas).
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Date: 2004-05

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