"Kashiwara—Vergne operads" (Guillaume Laplante-Anfossi, Melbourne)

12.08.2024 11:30 – 12:30

Gluing genus zero surfaces along boundaries endows their mapping class groups with the structure of an operad. A deep theorem of Boavida de Brito, Horel and Robertson from 2017 identifies the homotopy automorphisms of this operad with the Grothendieck—Teichmüller group, a mysterious profinite group containing the absolute Galois group of the rational numbers.

Intersecting loops on genus zero surfaces defines a Lie bialgebra structure on their fundamental groups, called the Goldman—Turaev Lie bialgebra. Around the same time, Alekseev, Kawazumi, Kuno and Naef defined group homomorphisms from the Grothendieck—Teichmüller group to the group formed by some special tangential automorphisms of the Lie bialgebra associated with any genus zero surface.

Are these two results related? I will describe ongoing joint work with Zsuzsanna Dancso, Iva Halacheva and Marcy Robertson, where we show that the tangential automorphisms known as Kashiwara—Vergne solutions, as well as their two symmetry groups, form operads. I will also mention what we know so far about their precise relationship to the Grothendieck—Teichmüller group.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05

entrée libre