Ellipsoid embeddings and symplectic packing stability

TL;DR

This paper establishes packing stability for closed symplectic manifolds with rational cohomology, providing new embedding results for ellipsoids and bounds for capacities that ensure volume-preserving embeddings in four dimensions.

Contribution

It introduces a general symplectic embedding theorem for ellipsoids and demonstrates packing stability for a broad class of symplectic manifolds, with computable bounds for capacities.

Findings

Packing stability holds for all closed symplectic manifolds with rational cohomology.

New embedding results for ellipsoids depend only on volume and thinness conditions.

Provides bounds for Embedded Contact Homology capacities ensuring volume-preserving embeddings in dimension 4.

Abstract

We prove packing stability for any closed symplectic manifold with rational cohomology class. 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 volume preserving embeddings in dimension 4.