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The cohomology ring of the GKM graph of a flag manifold of classical type
If a closed smooth manifold with an action of a torus satisfies
certain conditions, then a labeled graph \mG_M with labeling in is
associated with , which encodes a lot of geometrical information on . For
instance, the "graph cohomology" ring \mHT^*(\mG_M) of \mG_M is defined to
be a subring of \bigoplus_{v\in V(\mG_M)}H^*(BT), where V(\mG_M) is the set
of vertices of \mG_M, and is known to be often isomorphic to the equivariant
cohomology of . In this paper, we determine the ring structure of
\mHT^*(\mG_M) with (resp. ) coefficients when is a flag
manifold of type A, B or D (resp. C) in an elementary way.Comment: 22 page
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