Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

Abstract : We prove that the bihamiltonian cohomology of a semisimple pencil of Poisson brackets of hydrodynamic type vanishes for almost all degrees. This implies the existence of a full dispersive deformation of a semisimple bihamiltonian structure of hydrodynamic type starting from any infinitesimal deformation.
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Contributor : Imb - Université de Bourgogne <>
Submitted on : Wednesday, February 28, 2018 - 11:51:36 AM
Last modification on : Friday, October 19, 2018 - 10:56:15 AM

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Guido Carlet, Hessel Posthuma, Sergey Shadrin. Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed. Journal of Differential Geometry, International Press, 2018, 108 (1), pp.63-89. ⟨10.4310/jdg/1513998030⟩. ⟨hal-01719544⟩

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