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Ellipsoid embeddings and symplectic packing stability. (English) Zbl 1268.53092

Summary: 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” (ECH) capacities which are sufficient to imply the existence of some symplectic volume filling embeddings in dimension 4.

MSC:

53D35 Global theory of symplectic and contact manifolds
57R17 Symplectic and contact topology in high or arbitrary dimension
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References:

[1] doi:10.2140/gt.2011.15.2091 · Zbl 1239.53107 · doi:10.2140/gt.2011.15.2091
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