Proof of the Arnold chord conjecture in three dimensions II

2011/11/30 by Michael Hutchings, Clifford Henry Taubes · 1 citation
Mathematics · #math.SG

paper · pdf · doi:10.2140/gt.2013.17.2601

published as Geom. Topol. 17 (2013) 2601-2688 · v2 has minor corrections; to appear in Geometry and Topology

arxiv created 2013/06/05 · arxiv updated 2014/11/11

Abstract

In "Proof of the Arnold chord conjecture in three dimensions I", we deduced the Arnold chord conjecture in three dimensions from another result, which asserts that an exact symplectic cobordism between contact three-manifolds induces a map on (filtered) embedded contact homology satisfying certain axioms. The present paper proves the latter result, thus completing the proof of the three-dimensional chord conjecture. We also prove that filtered embedded contact homology does not depend on the choice of almost complex structure used to define it.

Cited by

• The Arnol'd chord conjecture for ST^*T³

Related

• Proof of the Arnold chord conjecture in three dimensions I
• Embedded contact homology and its applications
• Non-Exact Symplectic Cobordisms Between Contact 3-Manifolds
• Cobordism maps in embedded contact homology
• On Symplectic Cobordisms