Lie group action on a GKM manifold (Manifold Atlas Writing Seminar)

Manifold Atlas Writing Seminar
https://www.mpim-bonn.mpg.de/node/5242)

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.
In the first half, I will give a brief survey of GKM manifold. Then in the second half, I will discuss the case when the torus action extends to a Lie group action, and see how the action is reflected
on the combinatorial structure of the GKM graph.