The cohomology ring of the GKM graph of a flag manifold of classical type

الأصل · EN

If a closed smooth manifold M with an action of a torus T satisfies certain conditions, then a labeled graph ₘ with labeling in H²(BT) is associated with M, which encodes a lot of geometrical information on M. For instance, the "graph cohomology" ring (ₘ) of ₘ is defined to be a subring of ∈ V(ₘ)H*(BT), where V(ₘ) is the set of vertices of ₘ, and is known to be often isomorphic to the equivariant cohomology H*ₜ(M) of M. In this paper, we determine the ring structure of (ₘ) with (resp. [1/2]) coefficients when M is a flag manifold of type A, B or D (resp. C) in an elementary way.