A Quantitative Look at Lagrangian Cobordisms
A Quantitative Look at Lagrangian Cobordisms
Please note special day and time.听 听Lagrangian cobordisms between Legendrian submanifolds arise in Relative Symplectic Field Theory. In recent years, there has been much progress on answering qualitative questions such as: For a fixed pair of Legendrians, does there exist a Lagrangian cobordism? 听I will address two quantitative questions about Lagrangian cobordisms: 听For a fixed pair of Legendrians, what is the minimal 鈥渓ength鈥 of a Lagrangian cobordism? 听What is the relative Gromov width of a Lagrangian cobordism? Regarding length, I will give examples of pairs of Legendrians where Lagrangian cobordisms are flexible in that the non-cylindrical region can be arbitrarily short; I will also give examples of other pairs of Legendrians where Lagrangian cobordisms are rigid in that there is a positive lower bound to their length. For the second quantitative measure, I will give some calculations and estimates of the relative Gromov width of particular Lagrangian cobordisms. 听This is joint work with Joshua M. Sabloff.