/ Florian Naef: “String topology and the configuration space of two points”

Florian Naef: “String topology and the configuration space of two points”

September 17, 2019
4:30 pm - 5:30 pm
Abstract: Let M be a manifold with non-vanishing vector field. The homology of the space of loops in M carries a natural Lie bialgebra structure described by Sullivan as string topology operations. If M is a surface, these operations were originally defined by Goldman and Turaev. We study formal descriptions of these Lie bialgebras. More precisely, for surfaces these Lie bialgebras are formal in the sense that they are isomorphic (after completion) to their algebraic analogues (Schedler’s necklace Lie bialgebras) built from the homology of the surface and such isomorphisms are closely related to the Grothendieck–Teichm├╝ller group. For higher dimensional manifolds we give a similar description that turns out to depend on the Chern-Simons partition function. This talk is based on joint work with A. Alekseev, N. Kawazumi, Y. Kuno and T. Willwacher.