The Hofer question on intermediate symplectic capacities

Abstract

Roughly twenty five years ago Hofer asked: can the cylinder B^2(1) \times \mathbb{R}^{2(n-1)} be symplectically embedded into B^{2(n-1)}(R) \times \mathbb{R}^2 for some R>0? We show that this is the case if R \geq \sqrt{2^{n-1}+2^{n-2}-2}. We deduce that there are no intermediate capacities, between 1-capacities, first constructed by Gromov in 1985, and n-capacities, answering another question of Hofer. In 2008, Guth reached the same conclusion under the additional hypothesis that the intermediate capacities should satisfy the exhaustion property.

Main theorems and their proofs unchanged. Results not needed for these proofs removed for clarity (and posted as a separate paper). Title changed to emphasize main results. 21 pages, 7 figures

References in corpus (3)

• New obstructions to symplectic embeddings
• Recent progress on symplectic embedding problems in four dimensions
• Symplectic embeddings of polydisks

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