Lorenz knots are prime

Abstract

AbstractLorenz knots are the periodic orbits of a certain geometrically defined differential equation in ℝ3. This is called the ‘geometric Lorenz attractor’ as it is only conjecturally the real Lorenz attractor. These knots have been studied by the author and Joan Birman via a ‘knot-holder’, i.e. a certain branched two-manifold H. To show such knots are prime we suppose the contrary which implies the existence of a splitting sphere, S2. The technique of the proof is to study the intersection S2∩H. A novelty here is that S2∩H is likewise branched.