Recent progress on symplectic embedding problems in four dimensions.
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- Record sourced from PubMed, PMID 21518893.
- Also identified by DOI 10.1073/pnas.1018622108 and PMC identifier 3100991.
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Abstract
We survey some recent progress on understanding when one four-dimensional symplectic manifold can be symplectically embedded into another. In 2010, McDuff established a number-theoretic criterion for the existence of a symplectic embedding of one four-dimensional ellipsoid into another. This result is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball. Numerical invariants defined using embedded contact homology give general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases.