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Journal Articles Journal of Geometry and Physics Year : 2017

Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets

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.

Dates and versions

hal-01660609 , version 1 (11-12-2017)

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Guido Carlet, Matteo Casati, Sergey Shadrin. Poisson cohomology of scalar multidimensional Dubrovin–Novikov brackets. Journal of Geometry and Physics, 2017, 114, pp.404 - 419. ⟨10.1016/j.geomphys.2016.12.008⟩. ⟨hal-01660609⟩
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