Title: Twisted generating functions and the nearby Lagrangian conjecture
Speaker: Sylvain Courte
Speaker Info: Université Grenoble Alpes
Brief Description: Virtual (Zoom) Talk
Meeting ID: 916 7431 9341Date: Thursday, June 03, 2021
Meeting Password: First word of the name of the seminar (in small letters)
Abstract: 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.