Geometry & Topology

Proof of the Arnold chord conjecture in three dimensions, II

Michael Hutchings and Clifford Taubes

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Abstract

In “Proof of the Arnold chord conjecture in three dimensions, I” [Math. Res. Lett. 18 (2011) 295–313], 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.

Article information

Source
Geom. Topol., Volume 17, Number 5 (2013), 2601-2688.

Dates
Received: 15 November 2011
Accepted: 8 February 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732685

Digital Object Identifier
doi:10.2140/gt.2013.17.2601

Mathematical Reviews number (MathSciNet)
MR3190296

Zentralblatt MATH identifier
06213062

Subjects
Primary: 53D40: Floer homology and cohomology, symplectic aspects 57R58: Floer homology

Keywords
chord conjecture embedded contact homology Seiberg–Witten Floer

Citation

Hutchings, Michael; Taubes, Clifford. Proof of the Arnold chord conjecture in three dimensions, II. Geom. Topol. 17 (2013), no. 5, 2601--2688. doi:10.2140/gt.2013.17.2601. https://projecteuclid.org/euclid.gt/1513732685


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