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Contact topology and hydrodynamics III: knotted flowlines

By John Etnyre and Robert Ghrist


Abstract. We employ the relationship between contact structures and Beltrami fields derived in part I of this series to construct a steady nonsingular solution to the Euler equations on a Riemannian S 3 whose flowlines trace out closed curves of all possible knot and link types. Using careful contact-topological controls, we can make such vector fields realanalytic and transverse to the tight contact structure on S 3. Sufficient review of concepts is included to make this paper independent of the previous works in this series. 1

Year: 1999
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