Recent progress on symplectic embedding problems in four dimensions

Details Recent progress on symplectic embedding problems in four dimensions Recent progress on symplectic embedding problems in four dimensions

2011-01-05

arxiv.org/abs/1101.1069v2

Mathematics

Symplectic Geometry

updated bibliography, corrected typos, to appear in PNAS

Scientific paper

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 is related to previously known criteria for when a disjoint union of balls can be symplectically embedded into a ball. The new theory of "ECH capacities" gives general obstructions to symplectic embeddings in four dimensions which turn out to be sharp in the above cases.

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