Mathematical Research Letters

Volume 18 (2011)

Number 2

Proof of the Arnold chord conjecture in three dimensions I

Pages: 295 – 313



Michael Hutchings (Department of Mathematics, University of California at Berkeley, Berkeley CA 94720)

Clifford Henry Taubes (Mathematics Department, Harvard University, Cambridge MA 02138)


This paper and its sequel prove that every Legendrian knot in a closed three-manifold with a contact form has a Reeb chord. The present paper deduces this result from another theorem, asserting that an exact symplectic cobordism between contact 3-manifolds induces a map on (filtered) embedded contact homology satisfying certain axioms. The latter theorem will be proved in the sequel using Seiberg-Witten theory.

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