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Séminaire de Mathématique
# Cours -- Symmetries of Poisson Brackets: The Graph Complex and Orientation Morphism

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

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

Description

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.

Organized by

Maxim Kontsevich

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