University of Georgia
Mathematics Department Colloquium
Margaret Symington
University of Texas, Austin
January 8, 1999
Four dimensions from two: symplectic surgery and singularities
Abstract:
In dimension four, some of the simplest and yet most useful examples
of closed symplectic manifolds are those which are toric, i.e. admit
an effective Hamiltonian torus action. Remarkably, the moment map allows
one to completely describe a toric four-manifold by a subset of R^2.
A central theme in the work I have done is to use the moment map
for torus actions that are defined only locally, in conveniently chosen
neighborhoods. This idea has proved useful for devising surgery
constructions that yield interesting symplectic manifolds. Together
with the notion of symplectic convexity it may also provide insight
into singularities that could naturally be called symplectic.
After a brief primer on torus actions and the moment map, I will
describe these two applications.