pith. sign in

arxiv: 1210.1537 · v3 · pith:GGNRIFSAnew · submitted 2012-10-04 · 🧮 math.SG · math.DS

The Hofer question on intermediate symplectic capacities

classification 🧮 math.SG math.DS
keywords capacitieshoferintermediatemathbbquestiontimesadditionalanother
0
0 comments X
read the original 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.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.