# Twisted generating functions and the nearby Lagrangian conjecture

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Sylvain Courte, Université Grenoble Alpes

(Part of the Generating Functions Day joint with Western Hemisphere Virtual Symplectic Seminar)

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.