On symplectic geometry of tangent bundles of Hermitian symmetric spaces

2024/06/24 by Johanna Bimmermann, Bimmermann, Johanna
Biochemistry, Genetics and Molecular Biology · Mathematics · #14J42 #32M15 #53D20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Microtubule and mitosis dynamics #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2406.16440

openalex publication_date 2024/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explicitly construct a symplectomorphism that relates magnetic twists to the invariant hyperkähler structure of the tangent bundle of a Hermitian symmetric space. This symplectomorphism reveals foliations by (pseudo-) holomorphic planes, predicted by vanishing of symplectic homology. Furthermore, in the spirit of Weinstein's tubular neighborhood theorem, we extend the (Lagrangian) diagonal embedding of a compact Hermitian symmetric space to an open dense embedding of a specified neighborhood of the zero section. Using this embedding, we compute the Gromov width and Hofer-Zehnder capacity of these neighborhoods of the zero section.

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