This Thursday at U. Haifa Topology & Geometry seminar on March 28, 2019 at 12:10
Geometry & Topology Seminar
Speaker: Douglas Schultz (Technion)
Topic: A FAMILY OF NON- DISPLACEABLE LAGRANGIANS
IN A FULL FLAG MANIFOLD
Place: room 614 in the Science & Education Building
Date: Thursday, March 28, 2019
A symplectic manifold has no local invariants by Darboux’s theorem, so one is inclined to search for global invariants. It is known that certain Lagrangian submanifolds, which are half-dimensional submanifolds that are isotropic with respect to the symplectic form, say something deep about the ambient symplectic manifold. The Lagrangians that carry such information are all non-displaceable under exact isotopy of the symplectic manifold. However, these non-displaceable Lagrangians typically occur in discrete families, if we find them at all.
There are only a few examples in the literature of higher dimensional families of non-displaceable Lagrangians. In this talk, we exhibit such a family in manifold of full flags in C^3 by viewing said manifold as a symplectic fiber bundle and computing Floer homological invariants defined in this setting.