Proof of the Arnold chord conjecture in three dimensions I

Details Proof of the Arnold chord conjecture in three dimensions I Proof of the Arnold chord conjecture in three dimensions I

2010-04-25

arxiv.org/abs/1004.4319v3

Mathematics

Symplectic Geometry

minor corrections and clarifications, to appear in Mathematical Research Letters

Scientific paper

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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