Central invariants revisited
[Les invariants centraux revisités]
Carlet, Guido1 ; Kramer, Reinier2 ; Shadrin, Sergey2
1 Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne Franche-Comté 21000 Dijon, France
2 Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam Postbus 94248, 1090GE Amsterdam, Nederland
Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 149-175.

Nous utilisons des arguments raffinés de suite spectrale pour calculer des groupes de cohomologie bihamiltonienne, certains déjà connus et d’autres non, qui gouvernent la théorie des déformations de pinceaux bihamiltoniens semi-simples de type hydrodynamique avec une variable indépendante et N variables dépendantes. En particulier, nous retrouvons le résultat de Dubrovin-Liu-Zhang disant que ces déformations sont paramétrées par les invariants centraux, qui sont N fonctions lisses d’une variable.

We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamiltonian pencils of hydrodynamic type with one independent and N dependent variables. In particular, we rederive the result of Dubrovin-Liu-Zhang that these deformations are parametrized by the so-called central invariants, which are N smooth functions of one variable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/jep.66
Classification : 37K10, 53D17, 58A20
Keywords: Poisson structures of hydrodynamic type, deformations of bi-Hamiltonian structures, bi-Hamiltonian cohomology, central invariants
Mot clés : Structures de Poisson de type hydrodynamique, déformations de structures bihamiltoniennes, cohomologie bihamiltonienne, invariants centraux
Carlet, Guido 1 ; Kramer, Reinier 2 ; Shadrin, Sergey 2

1 Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université de Bourgogne Franche-Comté 21000 Dijon, France
2 Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam Postbus 94248, 1090GE Amsterdam, Nederland 
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Carlet, Guido; Kramer, Reinier; Shadrin, Sergey. Central invariants revisited. Journal de l’École polytechnique — Mathématiques, Tome 5 (2018), pp. 149-175. doi : 10.5802/jep.66. http://archive.numdam.org/articles/10.5802/jep.66/

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