Schipper, Floor (2024) Kontsevich (micro-)graph invariants in the geometry of Nambu-Poisson brackets: their nature and constraints. Master's Thesis / Essay, Mathematics.
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Abstract
Kontsevich constructed a map between ‘good’ graph cocycles γ and infinitesimal deformations of Poisson bivectors on affine manifolds, that is, Poisson cocycles in the second Lichnerowicz–Poisson cohomology. We call the infinitesimal deformation Qγ(P) trivial if there exists a vector field X⃗ such that Qγ(P) = JP, X⃗ K. For the class of Nambu-determinant Poisson brackets we establish that the known trivializing vector fields (also created from graphs) X⃗ γ3 2D, X⃗ γ3 3D, X⃗ γ3 4D and X⃗ γ5 2D are unique up to Hamiltonian vector fields. Moreover, we discuss the non-uniqueness of the choice of graphs to represent multivectors, and ideas that stem from this observation. Finally, we present a conjecture on the general form of the trivializing vector fields of Qγ3 (P) for all finite dimensions, where P is a Nambu-determinant Poisson bracket.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Kiselev, A.V. and Seri, M. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 03 Dec 2024 09:14 |
| Last Modified: | 03 Dec 2024 09:14 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/34441 |
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