Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed

2015/01/31 by Guido Carlet, Hessel Posthuma, Sergey Shadrin · 23 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Cohomology #Deformation (meteorology) #Homotopy and Cohomology in Algebraic Topology #Infinitesimal #Mathematical analysis #Mathematics #Nonlinear Waves and Solitons #Pencil (optics) #Physics #Poisson distribution #Poisson manifold #Poisson's ratio #Pure mathematics #Quantum mechanics #Type (biology) #math-ph #math.DG #math.MP #nlin.SI

paper · pdf · doi:10.4310/jdg/1513998030

published in Journal of Differential Geometry 108(1) (Lehigh University) · 22 pages. v2: corrected typos. v3: small improvements of the presentation. v4: typos, small improvements in the introduction and the presentation

arxiv created 2017/04/05 · openalex publication_date 2017/12/23 · arxiv updated 2018/10/23 · openalex created_date 2020/11/23 · openalex updated_date 2026/08/05

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.

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Deformations of bi-Hamiltonian structures of hydrodynamic type

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