Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets

2015/12/31 by Guido Carlet, Matteo Casati, Sergey Shadrin · 14 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Bracket #Cohomology #Equivariant cohomology #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Nonlinear Waves and Solitons #Novikov self-consistency principle #Poisson bracket #Poisson distribution #Pure mathematics #Scalar (mathematics) #Statistics #math-ph #math.DG #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.geomphys.2016.12.008

published in Journal of Geometry and Physics 114, 404-419 (Elsevier BV) · 23 pages. Typos corrected, add explicit form of homotopy contraction operator

openalex created_date 2016/06/24 · arxiv created 2016/12/12 · openalex publication_date 2016/12/22 · arxiv updated 2018/10/23 · openalex updated_date 2026/08/05

Abstract

We compute the Poisson cohomology of a scalar Poisson bracket of Dubrovin-Novikov type with D independent variables. We find that the second and third cohomology groups are generically non-vanishing in D>1. Hence, in contrast with the D=1 case, the deformation theory in the multivariable case is non-trivial.

Citations

• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• On Deformation of Poisson Manifolds of Hydrodynamic Type

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