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arXiv · 1210.1537

The Hofer question on intermediate symplectic capacities

Alvaro Pelayo·San Vu Ngoc
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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.

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Alvaro Pelayo, San Vu Ngoc. 2013-03-28. The Hofer question on intermediate symplectic capacities. https://doi.org/10.1112/plms%2Fpdu066

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