The translation number and quasi-morphisms on groups of symplectomorphisms of the disk

2019/12/23 by Shuhei Maruyama, Maruyama, Shuhei
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1912.10863

openalex publication_date 2019/12/23 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

Abstract

On groups of symplectomorphisms of the disk, we construct two homogeneous quasi-morphisms which relate to the Calabi invariant and the flux homomorphism respectively. We also show the relation between the quasi-morphisms and the translation number introduced by Poincaré.

Related

• Extensions of quasi-morphisms to the symplectomorphism group of the disk
• Quasi-Total Orders and Translation Numbers
• G-invariant quasimorphisms and symplectic geometry of surfaces
• Quasi-morphisms and quasi-states in symplectic topology
• Calabi quasimorphisms for the symplectic ball