Magnetic billiards and the Hofer-Zehnder capacity of disk tangent bundles of lens spaces

Abstract

We compute the Hofer-Zehnder capacity of disk tangent bundles of certain lens spaces with respect to the round metric. Interestingly we find that the Hofer-Zehnder capacity does not see the covering, i.e. the capacity of the disk tangent bundle of the lens space coincides with the capacity of the disk tangent bundle of the 3-sphere covering it. In particular, this gives a first example, where Gromov width and Hofer-Zehnder capacity of a disk tangent bundle disagree. Techniques we use include for the lower bound magnetic billiards and for the upper bound Gromov-Witten invariants.

23 pages, 5 figures. v2 has small corrections and improvements to exposition. Comments are welcome!

References in corpus (3)

• Symplectic embeddings into disk cotangent bundles
• Symplectic capacities of disc cotangent bundles of flat tori
• The Hopf-Rinow theorem and the Mañé critical value for magnetic geodesics on odd-dimensional spheres