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arXiv · 2207.11380

Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph

Shintaro Kuroki·Grigory Solomadin
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Abstract

In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the "leg bundle". We also provide a definition for the projectivization of a leg bundle and prove the Borel-Hirzebruch type formula for its graph equivariant cohomology, assuming that the projectivization is again a GKM graph. Furthermore, we study the realization of the projective GKM fiber bundle, in the sense of Guillemin-Sabatini-Zara, can be obtained from the projectivization of a leg bundle.

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Shintaro Kuroki, Grigory Solomadin. 2022-07-23. Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph. https://arxiv.org/abs/2207.11380

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