Proof of the Arnold chord conjecture in three dimensions, II

Hutchings, Michael¹ ; Taubes, Clifford²

¹ Mathematics Department, University of California, Berkeley, 970 Evans Hall, Berkeley, CA 94720, USA
² Department of Mathematics, Harvard University, Cambridge, MA 02138, USA

Geometry & topology, Tome 17 (2013) no. 5, pp. 2601-2688.

Résumé

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.

Détail

DOI : 10.2140/gt.2013.17.2601

Classification : 53D40, 57R58
Keywords: chord conjecture, embedded contact homology, Seiberg–Witten Floer

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