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

Text
Anass_Bouisaghouane_2017_WM.pdf  Published Version Download (1MB)  Preview 

Text
Toestemming.pdf  Other Restricted to Backend only Download (78kB) 
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 bivectors. In collaboration with R. Buring and A.V. Kiselev, we prove that the Kontsevich tetrahedral flow infinitesimally preserves the space of Poisson bivectors on all ndimensional 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 Poissoncohomology 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:  http://fse.studenttheses.ub.rug.nl/id/eprint/14910 
Actions (login required)
View Item 