no. 5
The translation number and quasi-morphisms on groups of symplectomorphisms of the disk
[Le nombre de translation et les quasi-morphismes sur des groupes de symplectomorphismes du disque]
Maruyama, Shuhei1
1 Nagoya University, Graduate School of Mathematics, Furocho, Chikusaku, Nagoya (Japan)
Annales de l'Institut Fourier, Tome 72 (2022) no. 5, pp. 1819-1830.

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.

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.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3487
Classification : 20J06, 37E45, 37E30
Keywords: quasi-morphism, bounded cohomology, symplectomorphism group
Mot clés : quasi-morphisme, cohomologie bornée, groupe des difféomorphismes symplectiques
Maruyama, Shuhei 1

1 Nagoya University, Graduate School of Mathematics, Furocho, Chikusaku, Nagoya (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Maruyama, Shuhei. The translation number and quasi-morphisms on groups of symplectomorphisms of the disk. Annales de l'Institut Fourier, Tome 72 (2022) no. 5, pp. 1819-1830. doi : 10.5802/aif.3487. https://aif.centre-mersenne.org/articles/10.5802/aif.3487/

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