Proof of the Arnold chord conjecture in three dimensions, II

Hutchings, Michael; Taubes, Clifford

doi:10.2140/gt.2013.17.2601

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Proof of the Arnold chord conjecture in three dimensions, II

Michael Hutchings and Clifford Henry Taubes

Geometry & Topology 17 (2013) 2601–2688

DOI: 10.2140/gt.2013.17.2601

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.

Keywords

chord conjecture, embedded contact homology, Seiberg–Witten Floer

Mathematical Subject Classification 2010

Primary: 53D40, 57R58

References

Publication

Received: 15 November 2011

Accepted: 8 February 2013

Published: 23 September 2013

Proposed: Tom Mrowka

Seconded: Peter Ozsváth, Leonid Polterovich

Authors

Michael Hutchings
Mathematics Department University of California, Berkeley 970 Evans Hall Berkeley, CA 94720 USA
http://math.berkeley.edu/~hutching
Clifford Henry Taubes
Department of Mathematics Harvard University Cambridge, MA 02138 USA

Volume 17, issue 5 (2013)