Topology Seminar Series: Emmy Murphy, MIT

Emmy Murphy, MIT

Title: Lagrangian Caps in High Dimensional Symplectic Manifolds
Speaker: Emmy Murphy, MIT
Date: Thursday, February 28, 2013
Time: 11:30am – 12:45pm
Place: Lecture Hall 102, Simons Center




Abstract: I will present a recent result (joint with Yakov Eliashberg) demonstrating the existence of exact Lagrangian cobordisms with a loose Legendrian in the negative end, in all dimensions greater than 4. In particular we show that there exists a Lagrangian disk in \C^n \ B^{2n} which has Legendrian boundary in S^{2n-1}, whenever n>2. It is known there are no such disks in \C^2. The proof showcases a new “Lagrangian Whitney trick”. As an application, we prove a universal embedding theorem for flexible Weinstein manifolds, showing in particular that any Weinstein manifold has interesting geometry only in a topological collar of the boundary. We also construct exact Lagrangian immersions with fewer intersections than the “philosophy of the Arnold conjecture” would predict (this application is joint with Tobias Ekholm, Eliashberg, and Ivan Smith).