Central invariants revisited

Abstract

We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamiltonian pencils of hydrodynamic type with one independent and \( N\) dependent variables. In particular, we rederive the result of Dubrovin-Liu-Zhang that these deformations are parametrized by the so-called central invariants, which are \( N\) smooth functions of one variable.

Accepted for publication in Journal de l'École polytechnique - Mathématiques

References in corpus (3)

• Deformations of semisimple Poisson pencils of hydrodynamic type are unobstructed
• Deformations of non semisimple Poisson pencils of hydrodynamic type
• The bi-Hamiltonian cohomology of a scalar Poisson pencil

Cited by in corpus (6)

• Towards a bihamiltonian structure for the double ramification hierarchy
• Higher genera Catalan numbers and Hirota equations for extended nonlinear Schroedinger hierarchy
• Variational Bihamiltonian Cohomologies and Integrable Hierarchies I: Foundations
• Miura-reciprocal transformations and localizable Poisson pencils
• Poisson pencils: reduction, exactness, and invariants
• Normal forms of dispersive scalar Poisson brackets with two independent variables