Proof of the Arnold chord conjecture in three dimensions I
Symplectic Geometry
2011-01-10 v3
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.
Keywords
Cite
@article{arxiv.1004.4319,
title = {Proof of the Arnold chord conjecture in three dimensions I},
author = {Michael Hutchings and Clifford Henry Taubes},
journal= {arXiv preprint arXiv:1004.4319},
year = {2011}
}
Comments
minor corrections and clarifications, to appear in Mathematical Research Letters