Geometry and Topology Seminar

Friday, March 24, 2017 2:30 pm - 2:30 pm EDT (GMT -04:00)

Charlotte Kirchoff-Lukat, University of Cambridge

"Lagrangian branes with boundary in stable generalised complex manifolds"

Generalised complex geometry interpolates between ordinary symplectic and complex manifolds. Stable generalised complex manifolds (first introduced by Cavalcanti, Gualtieri in 2015) carry a Poisson structure which is generically symplectic, but degenerates on a (real) codimension-2 submanifold. Half-dimensional generalised complex branes are distinguished submanifolds of generalised complex manifolds, and in a stable generalised complex manifold, they are generically Lagrangian. I will introduce a new type of generalised complex brane: Lagrangian branes with boundary. These branes do not intersect the degeneracy locus of the stable generalised complex structure transversely; instead the intersection is their boundary. This new type of generalised complex plane is thought to take the place of Lefschetz thimbles in the stable generalised complex analogue of Lefschetz fibrations, and would thus be needed to define their Fukaya category.

MC 5413