Equivariant K-theory of GKM bundles
Given a fiber bundle of GKM spaces, π: M → B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, π, into a fiber bundle of GKM graphs and constructing, by combinatorial techniques, a basis of this module consisting of K-classes which are invariant under the natural holonomy action on the K-ring of M of the fundamental group of the GKM graph of B. We also discuss the implications of this result for fiber bundles π: M → B where M and B are generalized partial flag varieties and show how our GKM description of the equivariant K-ring of a homogeneous GKM space is related to the Kostant–Kumar description of this ring.
KeywordsEquivariant K-theory Equivariant fiber bundles GKM manifolds Flag manifolds
Mathematics Subject ClassificationPrimary 55R91 Secondary 19L47 05C90
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- 3.Guillemin, V., Sabatini, S., Zara, C.: Balanced fiber bundles and GKM theory. (2012). arXiv: 1110.4086v1[math.AT]Google Scholar