# Proof of the Arnold chord conjecture in three dimensions, II

@article{Hutchings2013ProofOT,
title={Proof of the Arnold chord conjecture in three dimensions, II},
author={Michael Hutchings and Clifford H. Taubes},
journal={Geometry \& Topology},
year={2013},
volume={17},
pages={2601-2688}
}
• Published 25 April 2010
• Mathematics
• Geometry & Topology
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…
Proof of the Arnold chord conjecture in three dimensions I
• Mathematics
• 2011
In “Proof of the Arnold chord conjecture in three dimensions, I” [12], we deduced the Arnold chord conjecture in three dimensions from another result, which asserts that an exact symplectic cobordism
The asymptotics of ECH capacities
• Mathematics
• 2012
In a previous paper, the second author used embedded contact homology (ECH) of contact three-manifolds to define “ECH capacities” of four-dimensional symplectic manifolds. In the present paper we
Recent progress on symplectic embedding problems in four dimensions
• M. Hutchings
• Mathematics
Proceedings of the National Academy of Sciences
• 2011
Numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases.
Remarks about the C∞-closing lemma for 3-dimensional Reeb flows
We prove two refinements of theC∞-closing lemma for 3-dimensional Reeb flows, which was proved by the author as an application of spectral invariants ofEmbedded Contact Homology (ECH). Specifically,
On the Strict Arnold Chord Property and Coisotropic Submanifolds of Complex Projective Space
Let be a contact form on a manifoldM, and L M a closed Legendrian submanifold. I prove that L intersects some characteristic for at least twice if all characteristics are closed and of the same
Floer Homologies, with Applications
• Mathematics
Jahresbericht der Deutschen Mathematiker-Vereinigung
• 2018
Floer invented his theory in the mid eighties in order to prove the Arnol’d conjectures on the number of fixed points of Hamiltonian diffeomorphisms and Lagrangian intersections. Over the last thirty
S^1-equivariant contact homology for hypertight contact forms
• Mathematics
• 2019
In a previous paper, we showed that the original definition of cylindrical contact homology, with rational coefficients, is valid on a closed three-manifold with a dynamically convex contact form.
Lagrangian torus invariants using $ECH = SWF$
• Chris Gerig
• Mathematics
Journal of Symplectic Geometry
• 2021
We construct distinguished elements in the embedded contact homology (and monopole Floer homology) of a 3-torus, associated with Lagrangian tori in symplectic 4-manifolds and their isotopy classes.
The strict Arnold chord property for nicely embeddable regular contact forms
Let M be a manifold (possibly noncompact or with boundary) and α a contact form on M . We say that (M,α) has the strict chord property iff for every nonempty closed 1 Legendrian submanifold L ⊆ M
Embedded contact homology of prequantization bundles
• Mathematics
• 2020
The 2011 PhD thesis of Farris demonstrated that the ECH of a prequantization bundle over a Riemann surface is isomorphic as a Z/2Z-graded group to the exterior algebra of the homology of its base. We

## References

SHOWING 1-10 OF 34 REFERENCES
Proof of the Arnold chord conjecture in three dimensions I
• Mathematics
• 2011
In “Proof of the Arnold chord conjecture in three dimensions, I” [12], we deduced the Arnold chord conjecture in three dimensions from another result, which asserts that an exact symplectic cobordism
Embedded contact homology and its applications
Embedded contact homology (ECH) is a kind of Floer homology for contact three-manifolds. Taubes has shown that ECH is isomorphic to a version of Seiberg-Witten Floer homology (and both are
First steps in symplectic topology
CONTENTSIntroduction § 1. Is there such a thing as symplectic topology? § 2. Generalizations of the geometric theorem of Poincare § 3. Hyperbolic Morse theory § 4. Intersections of Lagrangian
The Weinstein conjecture for stable Hamiltonian structures
• Mathematics
• 2009
We use the equivalence between embedded contact homology and Seiberg-Witten Floer homology to obtain the following improvements on the Weinstein conjecture. Let Y be a closed oriented connected
An index inequality for embedded pseudoholomorphic curves in symplectizations
Abstract.Let Σ be a surface with a symplectic form, let φ be a symplectomorphism of Σ, and let Y be the mapping torus of φ. We show that the dimensions of moduli spaces of embedded pseudoholomorphic
The Chord Problem and a New Method of Filling by Pseudoholomorphic Curves
Let M be a closed three-dimensional manifold with contact form λ so that Ker λ is tight. In this paper, we will present a first application of the filling method by pseudoholomorphic curves recently
The embedded contact homology index revisited
Let Y be a closed oriented 3-manifold with a contact form such that all Reeb orbits are nondegenerate. The embedded contact homology (ECH) index associates an integer to each relative 2-dimensional
Embedded contact homology and Seiberg-Witten Floer cohomology I
This is the third of five papers whose purpose is to prove that the embedded contact homology of a compact, oriented 3–dimensional manifold with contact 1–form is isomorphic to the manifold’s
Gromov’s Compactness Theorem for Pseudo-holomorphic Curves
Mikhail Gromov introduced pseudo-holomorphic curves into symplectic geometry in 1985. This book aims to present in detail the original proof for Gromov's compactness theorum for pseudo-holomorphic
Algebraic Torsion in Contact Manifolds
• Mathematics
• 2010
We extract an invariant taking values in $${\mathbb{N}\cup\{\infty\}}$$ , which we call the order of algebraic torsion, from the Symplectic Field Theory of a closed contact manifold, and show that