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Contact topology and hydrodynamics III: knotted orbits


Authors: John Etnyre and Robert Ghrist
Journal: Trans. Amer. Math. Soc. 352 (2000), 5781-5794
MSC (2000): Primary 57M25, 37J55; Secondary 37C27, 76B47
DOI: https://doi.org/10.1090/S0002-9947-00-02651-9
Published electronically: August 8, 2000
MathSciNet review: 1781279
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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 real-analytic 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.


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Additional Information

John Etnyre
Affiliation: Department of Mathematics, Stanford University, Stanford, California, 94305
Email: etnyre@math.stanford.edu

Robert Ghrist
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: ghrist@math.gatech.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02651-9
Keywords: Tight contact structures, Reeb flows, Euler equations, knots, templates
Received by editor(s): June 29, 1999
Published electronically: August 8, 2000
Additional Notes: JE supported in part by NSF Grant # DMS-9705949.
RG supported in part by NSF Grant # DMS-9971629.
Article copyright: © Copyright 2000 American Mathematical Society

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