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

par Prof. Arthemy Kiselev (Groningen & IHES)

mercredi 27 nov. 2019, 14:00 → 17:15 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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.