Lie group action on a GKM manifold Seminar

A GKM manifold is a manifold with a "nice" torus action. Many interesting spaces are examples of GKM manifold including toric manifolds and flag manifolds.
Goresky-Kottwitz-MacPherson (for which GKM is an abbreviation) showed that
a certain kind of graph, called the GKM graph, is associated to a GKM manifold, from which we can read off the torus equivariant cohomology of the manifold purely combinatorially. I will discuss the case when the torus action extends to a Lie group action, and show how the action is reflected on the combinatorial structure of the GKM graph.