Balanced Fiber Bundles and GKM Theory
Let T be a torus and B a compact T-manifold. Goresky et al. show in  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-T). 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 pi:M -> B a fiber bundle for which pi intertwines the two T-actions, there is a simple combinatorial description of H-T*(M) as a subring of H-T*(pi(-1)(B-T)). Using this result, we obtain fiber bundle analogs of results of Guillemin et al.  on GKM theory for homogeneous spaces.