Balanced Fiber Bundles and GKM Theory

Let T be a torus and B a compact T-manifold. Goresky et al. show in [3] that if B is (what was subsequently called) a GKM manifold, then there exists a simple combinatorial description of the equivariant cohomology ring as a subring of . In this paper, we prove an analog 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 as a subring of . Using this result, we obtain fiber bundle analogs of results of Guillemin et al. [4] on GKM theory for homogeneous space