Séminaire de Géométrie et Quantification
On the Kashiwara-Vergne problem in higher genera and its connection to the Goldman-Turaev Lie bialgebra.
Résumé : Using the intersection and self-intersection of loops on a surface one can define the Goldman-Turaev Lie bialgebra, and its non-commutative double avatar. On a genus zero surface with three boundary components the linearization problem of this structure is equivalent to the Kashiwara-Vergne problem in Lie theory. Motivated by this result a generalization of the Kashiwara-Vergne problem in higher genera is proposed and solutions are constructed in analogy with elliptic associators defined by B. Enriquez. This is joint work with A. Alekseev, N. Kawazumi and Y. Kuno.