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.

22 pages. v2: corrected typos. v3: small improvements of the presentation. v4: typos, small improvements in the introduction and the presentation

References in corpus (1)

• The bi-Hamiltonian cohomology of a scalar Poisson pencil

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