Work

Kontsevich graphs act on Nambu–Poisson brackets, II. The tetrahedral flow is a coboundary in 4D

Year: 2024

Type: conference-paper

Abstract: Kontsevich constructed a map from suitable cocycles in the graph complex to infinitesimal deformations of Poisson bi-vector fields. Under the deformations, the bi-vector fields remain Poisson. We ask, are these deformations trivial, meaning, do they amount to a change of coordinates along a vector field? We examine this question for the tetrahedron, the smallest nontrivial suitable graph cocycle in the Kontsevich graph complex, and for the class of Nambu–Poisson brackets on ℝ d . Within Kontsevich’s graph calculus, we use dimension-specific micro-graphs, in which each vertex represents an ingredient of the Nambu–Poisson bracket. For the tetrahedron, Kontsevich knew that the deformation is trivial for d = 2 (1996). In 2020, Buring and the third author found that the deformation is trivial for d = 3. Building on these discoveries, we now establish that the deformation is trivial for d = 4.

Source: Journal of Physics Conference Series

DOI: 10.1088/1742-6596/2912/1/012042

Authors: Mollie S Jagoe Brown, Floor Schipper, Arthemy V Kiselev

Institution: University of Groningen

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Rijksuniversiteit Groningen

Award: G4196832238