Contents Online
Mathematical Research Letters
Volume 18 (2011)
Number 2
Proof of the Arnold chord conjecture in three dimensions I
Pages: 295 – 313
DOI: https://dx.doi.org/10.4310/MRL.2011.v18.n2.a8
Authors
Abstract
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.
Published 20 May 2011