Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids

Digiosia, Leo; Nelson, J. M.; Ning, Haoming; Weiler, Morgan; Yang, Yirong

doi:10.1007/s11784-022-00981-6

Cited by 1 publication

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“… 24 , theorem 1.19 that if

and

are four-dimensional convex toric domains, and if there exists a symplectic embedding

, then a certain combinatorial criterion holds. This leads to stronger symplectic embedding obstructions in some cases where ECH capacities do not give sharp obstructions, for example to symplectically embedding a polydisk into a ball or ellipsoid ( 24 , 26 , 27 ).…”

Section: Computation For Convex Toric Domainsmentioning

confidence: 99%

An elementary alternative to ECH capacities

Hutchings

2022

Proc. Natl. Acad. Sci. U.S.A.

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The embedded contact homology (ECH) capacities are a sequence of numerical invariants of symplectic four-manifolds that give (sometimes sharp) obstructions to symplectic embeddings. These capacities are defined using embedded contact homology, and establishing their basic properties currently requires Seiberg–Witten theory. In this paper we define a sequence of symplectic capacities in four dimensions using only basic notions of holomorphic curves. The capacities satisfy the same basic properties as ECH capacities and agree with the ECH capacities for the main examples for which the latter have been computed, namely convex and concave toric domains. The capacities are also useful for obstructing symplectic embeddings into closed symplectic four-manifolds. This work is inspired by a recent preprint of McDuff and Siegel [D. McDuff, K. Siegel, arXiv [Preprint] (2021)], giving a similar elementary alternative to symplectic capacities from rational symplectic field theory (SFT).

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“… 24 , theorem 1.19 that if

and

are four-dimensional convex toric domains, and if there exists a symplectic embedding

Section: Computation For Convex Toric Domainsmentioning

confidence: 99%