Stratified integrals and unknots in invicid flows
Joint work with Robert Ghrist.
Contemp. Math. 246 (1999), 99-111.

We prove that any steady solution to the real analytic Euler equations on a Riemannian three sphere must possess a periodic orbit bounding an embedded disc. One key ingredient is an extension of Fomenko's work on the topology of integrable Hamiltonian systems to a degenerate case involving stratified integrals. The result on the Euler equations follows from this when combined with some contact-topological perspectives and a recent result of Hofer, Wyzsocki, and Zehnder.

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