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.

23 pages. Typos corrected, add explicit form of homotopy contraction operator

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