EVENT DETAILS AND ABSTRACT

Title: The Goldman-Turaev Lie bialgebra and Kashiwara-Vergne
Speaker: Florian Naef
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Abstract:

The vector space spanned by the homotopy classes of free loops on a surface canonically carries the structure of a filtered Lie bialgebra. The bracket and cobracket were discovered by Goldman and Turaev, respectively. We address the question of identifying the associated graded Lie bialgebra.

In the genus zero case we show that there is a close relationship between this question and solutions to Kashiwara-Vergne. The proof uses Van den Bergh's formalism of double brackets and the theory of quasi-Poisson spaces.