Proof of the Arnold chord conjecture in three dimensions, II
By Michael Hutchings, Clifford H. Taubes. 2010
83 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/658eeaf0381eef6abd66ec170c71620e7ce790bf
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In Discrete Mathematics and Combinatorics
- Daniel Cristofaro-Gardiner
- V. G. B. Ramos
- Michael Hutchings
- Clifford H. Taubes
- Andrew Cotton-Clay
- Richard Siefring
- P. Seidel
- I. Smith
In Geometry and Topology
- Daniel Cristofaro-Gardiner
- Michael Hutchings
- V. G. B. Ramos
- Richard Siefring
- Clifford H. Taubes
- Andrew Cotton-Clay
- F. Schlenk
- Jean Gutt
In Mathematical Physics
- Daniel Cristofaro-Gardiner
- Michael Hutchings
- V. G. B. Ramos
- Richard Siefring
- Clifford H. Taubes
- Andrew Cotton-Clay
- F. Schlenk
- Jean Gutt
Citations in the corpus
- Beyond ECH capacities (2014, background): “It is shown in [15, Theorem 1.3] that filtered ECH does not depend on the choice of almost complex structure J .”
- The asymptotics of ECH capacities (2012, methodology): “Both arguments use Seiberg-Witten theory; in particular, Seiberg-Witten theory is used to define ECH cobordism maps in [10].”
- Lecture Notes on Embedded Contact Homology (2013, methodology): “17) in [32] instead counts solutions to the Seiberg-Witten equations, perturbed as in the proof of the isomorphism (1.”