We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semisimple 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.
Carlet, G., Kramer, R., Shadrin, S. (2018). Central invariants revisited. JOURNAL DE L'ÉCOLE POLYTECHNIQUE. MATHÉMATIQUES, 5, 149-175 [10.5802/jep.66].
Central invariants revisited
Carlet G.;Kramer R.;
2018
Abstract
We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semisimple 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.
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