Kai Cieliebak: Homological algebra related to surfaces with boundary

This talk reports on joint work with K.Fukaya, J.Latschev, and E.Volkov (in progress). Its aim is to describe the common algebraic structure arising in string topology, symplectic field theory, and higher genus Lagrangian Floer theory. This structure is an infinity version of an involutive Lie bialgebra. After a brief discussion of the homotopy theory of these structures, I will present a construction associating such a structure to every DGA using Feynman type sums over ribbon graphs. When applied to the de Rham algebra of a closed simply connected manifold this construction yields a chain-level version of string topology, though the precise relation is still not understood.