Séminaire de Mathématique

Cours -- Symmetries of Poisson Brackets: The Graph Complex and Orientation Morphism

by Prof. Arthemy Kiselev (Groningen & IHES)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette

Lecture 3

The graph orientation morphism: constructing a symmetry by using a graph cocycle.

 * Endomorphisms of the space of multivector fields. The Schouten bracket, its own Jacobi identity; the master-equation. The Richardson--Nijenhuis bracket, its own Jacobi identity; the master equation.

 * The edge (the stick in the construction of graph differential). The graph orientation morphism Or takes the stick to the Schouten bracket.

 * Verifying the property of the image of a graph cocycle under Or to be a Poisson cocycle. Canonical and incidental solutions of the problem of factorization via the Jacobiator. Topological identities in the spaces of Leibniz graphs.

 * Lie algebra homomorphism: from graph cocycles to symmetries of Poisson brackets.

Organized by

Maxim Kontsevich