Sutured ECH is a natural invariant

We show that sutured embedded contact homology is a natural invariant of sutured contact 3 3 -manifolds which can potentially detect some of the topology of the space of contact structures on a 3 3 -manifold with boundary. The appendix, by C. H. Taubes, proves a compactness result for the completion of a sutured contact 3 3 -manifold in the context of Seiberg–Witten Floer homology, which enables us to complete the proof of naturality.

Sub-leading asymptotics of ECH capacities

In previous work (Cristofaro-Gardiner et al. in Invent Math 199:187–214, 2015), the first author and collaborators showed that the leading asymptotics of the embedded contact homology spectrum recovers the contact volume. Our main theorem here is a new bound on the sub-leading asymptotics.

Ellipsoid embeddings and symplectic packing stability

We prove packing stability for rational symplectic manifolds. This will rely on a general symplectic embedding result for ellipsoids which assumes only that there is no volume obstruction and that the domain is sufficiently thin relative to the target. We also obtain easily computable bounds for the Embedded Contact Homology capacities which are sufficient to imply the existence of some symplectic volume filling embeddings in dimension 4.