The translation number and quasi-morphisms on groups of symplectomorphisms of the disk
Annales de l'Institut Fourier, Online first, 12 p.

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.

Sur des groupes de symplectomorphismes du disque, nous construisons deux quasi-morphismes homogènes reliés à l’invariant de Calabi et l’homomorphisme du flux respectivement. Nous montrons également la relation entre les quasi-morphismes et le nombre de translation introduit par Poincaré.

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Accepted:
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DOI: 10.5802/aif.3487
Classification: 20J06,  37E45,  37E30
Keywords: quasi-morphism, bounded cohomology, symplectomorphism group
Maruyama, Shuhei 1

1 Nagoya University, Graduate School of Mathematics, Furocho, Chikusaku, Nagoya (Japan)
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Maruyama, Shuhei. The translation number and quasi-morphisms on groups of symplectomorphisms of the disk. Annales de l'Institut Fourier, Online first, 12 p.

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