Ellipsoid embeddings and symplectic packing stability

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.

18 pages, 3 figures

References in corpus (5)

• Symplectic embeddings of 4-dimensional ellipsoids: erratum
• New obstructions to symplectic embeddings
• Symplectic embeddings of ellipsoids in dimension greater than four
• Polarizations and symplectic isotopies
• The generating function of the embedding capacity for 4-dimensional symplectic ellipsoids

Cited by in corpus (10)

• When symplectic topology meets Banach space geometry
• Ehrhart polynomials and symplectic embeddings of ellipsoids
• Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs
• The ghost stairs stabilize to sharp symplectic embedding obstructions
• Symplectic embeddings of 4-dimensional ellipsoids into polydiscs
• Irreversibility from staircases in symplectic embeddings
• Special eccentricities of rational four-dimensional ellipsoids
• Topology of symplectomorphism groups and ball-swappings
• Coarse-graining and symplectic non-squeezing
• Packing stability for symplectic $4$-manifolds