The Kontsevich tetrahedral flow and infinitesimal deformations of Poisson structures

Bouisaghouane, A. (2017) The Kontsevich tetrahedral flow and infinitesimal deformations of Poisson structures. Master's Thesis / Essay, Mathematics.

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Abstract

In the paper "Formality conjecture'' (1996) Kontsevich designed a universal flow, called the tetrahedral flow, on the spaces of Poisson structures on all affine manifolds of dimension at least 2. We investigate several claims made by Kontsevich in loc. cit. We reveal, by using several examples of Poisson structures, that, in general, it is only the balance 1:6 for which the flow preserves the space of Poisson bi-vectors. In collaboration with R. Buring and A.V. Kiselev, we prove that the Kontsevich tetrahedral flow infinitesimally preserves the space of Poisson bi-vectors on all n-dimensional affine manifolds if and only if the two differential monomials in the formula for the flow are balanced by the ratio a:b=1:6. We then investigate the triviality of the flow and prove that for n=2, the flow is Poisson-cohomology trivial: the flow is equal to the Schouten bracket of the initial Poisson structure and a vector field; we examine the space of solutions and its properties, and represent a specific solution by Kontsevich graphs.

Item Type:	Thesis (Master's Thesis / Essay)
Degree programme:	Mathematics
Thesis type:	Master's Thesis / Essay
Language:	English
Date Deposited:	15 Feb 2018 08:26
Last Modified:	15 Feb 2018 08:26
URI:	https://fse.studenttheses.ub.rug.nl/id/eprint/14910

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