Kontsevich graphs act on Nambu–Poisson brackets, IV. When the invisible becomes crucial
Year: 2025
Type: conference-paper
Abstract: Kontsevich’s graphs allow encoding multi-vectors whose coefficients are differential- polynomial in the coefficients of a given Poisson bracket on an affine real manifold. Encoding formulas by directed graphs adapts to the class of Nambu-determinant Poisson brackets, yet the graph topology becomes dimension-specific. To inspect whether a given Kontsevich graph cocycle γ acts (non)trivially – in the second Poisson cohomology – on the space of Nambu brackets, taking a vector field solution X → d γ from dimension d does not work in d + 1. For 2 ≤ d ≤ 4, the action of tetrahedron γ 3 on Nambu brackets is known to be a Poisson coboundary, P ˙ = 〚 P , X → d γ 3 ( P ) 〛 . We explore which minimal (sub)sets of graphs, encoding (non)vanishing objects over ℝ a f f d , generate the topological data that suffice for a solution X → d + 1 γ 3 to appear. We detect that there can be no solution in higher dimension without invisible graphs that vanish as formulas in d = 3, but whose descendants do not all vanish over d = 4.
Authors: Mollie S. Jagoe Brown, Arthemy V. Kiselev
Institution: University of Groningen
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417047180
FWCI:
Cites:
Cited by:
Related to: