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Title:
The Length and Width of Lagrangian Cobordisms
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Abstract:
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 between them? One can also ask quantitative questions: What is the “length” or “width” of a Lagrangian cobordism? 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. In addition, I will give some calculations of the relative Gromov width of particular Lagrangian cobordisms. This is joint work with Joshua M. Sabloff.
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