Proof of the Arnold chord conjecture in three dimensions I

2010/04/25 by Michael R. Hutchings, Clifford Henry Taubes, Hutchings, Michael +1 · 4 citations
Mathematics · Computer Science · #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1004.4319

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.

Cited by

• A homological criterion for the almost-existence of Hamiltonian chords
• Max-min energy of pseudoholomorphic curves and periodic Reeb flows in dimension 3
• ECH capacities of concave singular toric domains
• Wrapped Floer homology and subcritical handle attachment

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• A Proof On Arnold Chord Conjecture
• On the strong Arnold chord conjecture for convex contact forms
• Legendrian embedded contact homology
• Unknotted Reeb orbits and nicely embedded holomorphic curves
• Strong Arnold chord conjecture via normalized capacities