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- W2589275855 abstract "In the paper Formality conjecture (1996) Kontsevich designed a universal flow $dot{mathcal{P}}=mathcal{Q}_{a:b}(mathcal{P})=aGamma_{1}+bGamma_{2}$ on the spaces of Poisson structures $mathcal{P}$ on all affine manifolds of dimension $n geqslant 2$. We prove a claim from $textit{loc. cit.}$ stating that if $n=2$, the flow $mathcal{Q}_{1:0}=Gamma_{1}(mathcal{P})$ is Poisson-cohomology trivial: $Gamma_{1}(mathcal{P})$ is the Schouten bracket of $mathcal{P}$ with $mathcal{X}$, for some vector field $mathcal{X}$; we examine the structure of the space of solutions $mathcal{X}$. Both the construction of differential polynomials $Gamma_{1}(mathcal{P})$ and $Gamma_{2}(mathcal{P})$ and the technique to study them remain valid in higher dimensions $n geqslant 3$, but neither the trivializing vector field $mathcal{X}$ nor the setting $b:=0$ survive at $ngeqslant 3$, where the balance is $a:b=1:6$." @default.
- W2589275855 created "2017-03-03" @default.
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- W2589275855 date "2017-02-20" @default.
- W2589275855 modified "2023-09-27" @default.
- W2589275855 title "The Kontsevich tetrahedral flow in 2D: a toy model" @default.
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- W2589275855 hasPublicationYear "2017" @default.
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