Abstract
If a closed smooth manifold with an action of a torus satisfies certain conditions, then a labeled graph with labeling in is associated with , which encodes a lot of geometrical information on . For instance, the “graph cohomology” ring of is defined to be a subring of , where is the set of vertices of , and is known to be often isomorphic to the equivariant cohomology of . In this paper, we determine the ring structure of with (resp., ) coefficients when is a flag manifold of type A, B, or D (resp., C) in an elementary way.
Citation
Yukiko Fukukawa. Hiroaki Ishida. Mikiya Masuda. "The cohomology ring of the GKM graph of a flag manifold of classical type." Kyoto J. Math. 54 (3) 653 - 677, Fall 2014. https://doi.org/10.1215/21562261-2693478