Journal of Differential Geometry

Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

Guido Carlet, Hessel Posthuma, and Sergey Shadrin

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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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J. Differential Geom., Volume 108, Number 1 (2018), 63-89.

Received: 5 March 2015
First available in Project Euclid: 23 December 2017

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Carlet, Guido; Posthuma, Hessel; Shadrin, Sergey. Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed. J. Differential Geom. 108 (2018), no. 1, 63--89. doi:10.4310/jdg/1513998030.

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