Twisted generating functions and the nearby Lagrangian conjecture

I will explain the notion of twisted generating function and show that a closed exact Lagrangian submanifold LL in the cotangent bundle of MM admits such a thing. The type of function arising in our construction is related to Waldhausen's tube space from his manifold approach to algebraic K-theory of spaces. Using the rational equivalence of this space with BO, as proved by Bökstedt, we conclude that the stable Lagrangian Gauss map of LL vanishes on all homotopy groups. In particular when MM is a homotopy sphere, we obtain the triviality of the stable Lagrangian Gauss map and a genuine generating function for LL. This is a joint work with M. Abouzaid, S. Guillermou and T. Kragh.