Balanced Fiber Bundles and GKM Theory
نویسنده
چکیده
Let T be a torus and B a compact T−manifold. Goresky, Kottwitz, and MacPherson show in [GKM] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring H∗ T (B) as a subring of H∗ T (B ). In this paper we prove an analogue of this result for T−equivariant fiber bundles: we show that if M is a T−manifold and π : M → B a fiber bundle for which π intertwines the two T−actions, there is a simple combinatorial description of H∗ T (M) as a subring of H∗ T (π(B )). Using this result we obtain fiber bundle analogues of results of [GHZ] on GKM theory for homogeneous spaces.
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