Symplectic isotopy classes of ellipsoids and polydisks in dimension greater than four

Abstract

In any dimension $2n\ge 6$ we show that certain spaces of symplectic embeddings of a polydisk into a product $B^4\times {\mathbb{R}}^{2(n-2)}$ of a $4$-ball and Euclidean space, are not path connected. We also show that any pair of such nonisotopic embeddings can never be extended to the same ellipsoid.

Major correction and revision to the section on ellipsoids

References in corpus (3)

• Symplectic embeddings of 4-dimensional ellipsoids: erratum
• Nongeneric J-holomorphic curves and singular inflation
• Maximal Symplectic packings of ${\P }^2$