Invariant of the Legendrian lift of an exact Lagrangian submanifold in the circular contactization of a Liouville manifold

Abstract: Any exact Lagrangian submanifold in a Liouville manifold lifts to a Legendrian submanifold in the circular contactization. For the standard contact form, this Legendrian admits countably many Reeb chords (indexed by their winding number around the fiber) above each point, thus yielding a degenerate situation. In this talk, we will slightly perturb the contact form and compute the Chekanov-Eliashberg DG-algebra of the Legendrian lift in term of the Floer A_{\infty}-algebra of the Lagrangian. The main idea will be to view the Koszul dual of the DG-algebra as a particular homotopy colimit (as defined by Ganatra-Pardon-Shende) of A_{\infty}-categories.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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