Balanced Fiber Bundles and GKM Theory
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Guillemin_Balanced fiber.pdf
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Author(s)
Guillemin, Victor W.
Sabatini, Silvia
Zara, Catalin
Date Issued
July 2012
Journal
International Mathematics Research Notices
Publisher
Oxford University Press
Citation
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.
Version
Original manuscript
Abstract
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 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1093/imrn/rns168
