Séminaire de Mathématique

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

by Prof. Arthemy Kiselev (Groningen & IHES)

Europe/Paris
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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