Proof of the Arnold chord conjecture in three dimensions II

TL;DR

This paper completes the proof of the Arnold chord conjecture in three dimensions by establishing that an exact symplectic cobordism induces a suitable map on embedded contact homology, confirming the conjecture's validity.

Contribution

It proves that filtered embedded contact homology is independent of the almost complex structure and completes the proof of the Arnold chord conjecture in three dimensions.

Findings

Established the map on filtered embedded contact homology satisfies necessary axioms

Proved independence of filtered embedded contact homology from almost complex structure

Completed the proof of the Arnold chord conjecture in three dimensions

Abstract

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.