Joint GT-UGA Seminar at GT - Augmentations and immersed exact Lagrangian fillings by Yu Pan

Series: 
Geometry Topology Seminar
Monday, April 16, 2018 - 15:30
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
MIT
Organizer: 
Augmentations and exact Lagrangian fillings are closely related. However, not all the augmentations of a Legendrian knot come from embedded exact Lagrangian fillings. In this talk, we show that all the augmentations come from possibly immersed exact Lagrangian fillings. In particular, let ∑ be an immersed exact Lagrangian filling of a Legendrian knot in $J^1(M)$ and suppose it can be lifted to an embedded Legendrian L in J^1(R \times M). For any augmentation of L, we associate an induced augmentation of the Legendrian knot, whose homotopy class only depends on the compactly supported Legendrian isotopy type of L and the homotopy class of its augmentation of L. This is a joint work with Dan Rutherford.