Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar

I will explain the notion of twisted generating function and show that a closed exact Lagrangian submanifold $L$ in the cotangent bundle of $M$ 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 $L$ vanishes on all homotopy groups. In particular when $M$ is a homotopy sphere, we obtain the triviality of the stable Lagrangian Gauss map and a genuine generating function for $L$. This is a joint work with M. Abouzaid, S. Guillermou and T. Kragh.