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 …

This paper and its sequel prove that every Legendrian knot in a closed three-manifold with a
contact form has a Reeb chord. The present paper deduces this result from another theorem,
asserting that an exact symplectic cobordism between contact 3-manifolds induces a map
on (filtered) embedded contact homology satisfying certain axioms. The latter theorem will
be proved in the sequel using Seiberg-Witten theory.