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

Lecture 1

The structure of differential graded Lie algebra (dgLa) on the vector space of graphs with a wedge ordering of edges. « Zero graphs » = minus themselves. The vertex-blow-up differential, Lie bracket, its Jacobi identity. The determining properties of the complex (identities involving zero graphs).

 * Examples of nontrivial cocycles: the tetrahedron, 5-wheel + prism. The (2k+1)-wheels as markers of nontrivial cocycles originating from the Grothendieck–Teichmueller Lie algebra.