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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Proof of the Arnold chord conjecture in three dimensions, II

Michael Hutchings and Clifford Henry Taubes

Geometry & Topology 17 (2013) 2601–2688
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