2025/11/08 by M. Brown, Arthemy V. Kiselev, Brown, Mollie S. Jagoe +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2511.06121
Kontsevich's graphs from deformation quantisation allow encoding multi-vectors whose coefficients are differential-polynomial in components of Poisson brackets on finite-dimensional affine manifolds. The calculus of Kontsevich graphs can be made dimension-specific for the class of Nambu--Poisson brackets given by Jacobian determinants. Using the Kontsevich--Nambu micro-graphs in dimensions d\geqslant 2, we explore the open problem of (non)triviality for Kontsevich's tetrahedral graph cocycle action on the space of Nambu--Poisson brackets. We detect a conjecturally infinite new set of differential-polynomial identities for Jacobian determinants of arbitrary sizes d× d.