Claremont Topology Seminar: Wenyuan Li (USC)

Title: Generating families on Lagrangian cobordisms

Abstract: An important question in contact topology is to understand Legendrian knots and their relations given by Lagrangian cobordisms. In the contact manifold T*M x R, an important tool to study Legendrian knots and their Lagrangian cobordisms is called generating families or generating functions, which are generalizations of the defining functions f of graphical Legendrians of the form {(x, df(x), f(x))}. When there exists a generating family with good control at infinity, interesting Legendrian invariants can be extracted. We try to understand the following basic question: when can a generating function on the Legendrian knot be extended to the Lagrangian cobordism? We will give a necessary and sufficient condition to the problem for generating families with good control at infinity. In particular, we show that such an extension always exists in the case of Lagrangian concordances.