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arXiv · 1512.05744

Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets

Guido Carlet·Matteo Casati·Sergey Shadrin
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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.

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Guido Carlet, Matteo Casati, Sergey Shadrin. 2015-12-17. Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets. https://doi.org/10.1016/j.geomphys.2016.12.008

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