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Title:
The Goldman-Turaev Lie bialgebra and the Kashiwara-Vergne problem
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Abstract:
It is conjectured that several graded Lie algebras coming up in different fields of mathematics coincide: the Grothendieck-Teichmueller Lie algebra grt related to the braid group in 3d topology, the double shuffle Lie algebra ds in the theory of multiple zeta values and the Kashiwara-Vergne Lie algebra kv in Lie theory. We are adding one more piece to this puzzle: it turns out that the Kashiwara-Vergne Lie algebra plays an important role in the Goldman-Turaev theory defined in terms of intersections and self-intersections of curves on 2-manifolds. This allows to define the Kashiwara-Vergne problem for surfaces of arbitrary genus. In particular, we focus on the genus one case and discuss the relation between elliptic kv and elliptic grt. The talk is based on a joint work with N. Kawazumi, Y. Kuno and F. Naef
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