On the Hofer-Zehnder capacity for twisted tangent bundles over closed\n surfaces

2020/11/19 by Johanna Bimmermann, Bimmermann, Johanna
Mathematics · Physics and Astronomy · #37J39 #37J45 #53D05 #53D20 #53D35 #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2011.09828

openalex publication_date 2020/11/19 · openalex created_date 2023/11/11 · openalex updated_date 2026/07/28

Abstract

We determine the Hofer-Zehnder capacity for twisted tangent bundles over\nclosed surfaces for (i) arbitrary constant magnetic fields on the two-sphere\nand (ii) strong constant magnetic fields for higher genus surfaces. On S² we\nfurther give an explicit \SO(3)-equivariant compactification of the\ntwisted tangent bundle to S²\× S² with split symplectic form. The\nformer is the phase space of a charged particle moving on the two-sphere in a\nconstant magnetic field, the latter is the configuration space of two massless\ncoupled angular momenta.\n

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