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

DOI10.5802/AIF.3487arXiv1912.10863MaRDI QIDQ6331685

Publication date: 23 December 2019

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 Poincar'{e}.

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Cohomology of groups (20J06) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Canonical transformations in symplectic and contact geometry (53D22)

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