Balanced Fiber Bundles and GKM Theory
Author(s)Guillemin, Victor W.; Sabatini, Silvia; Zara, Catalin
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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*[over]T(B) as a subring of H*[over]T(B[superscript 2]). 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 H*[over]T(M) as a subring of H*[over]T(π[superscript -1](B[superscript T])). Using this result, we obtain fiber bundle analogs of results of Guillemin et al. on GKM theory for homogeneous spaces.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
International Mathematics Research Notices
Oxford University Press
Guillemin, V., S. Sabatini, and C. Zara. “Balanced Fiber Bundles and GKM Theory.” International Mathematics Research Notices (July 9, 2012). vol. 2013 (17): 3886-3910.