Annals of Global Analysis and Geometry

, Volume 43, Issue 1, pp 31–45 | Cite as

Equivariant K-theory of GKM bundles

Article

Abstract

Given a fiber bundle of GKM spaces, π: MB, 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: MB 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.

Keywords

Equivariant K-theory Equivariant fiber bundles GKM manifolds Flag manifolds 

Mathematics Subject Classification

Primary 55R91 Secondary 19L47 05C90 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Victor Guillemin
    • 1
  • Silvia Sabatini
    • 2
  • Catalin Zara
    • 3
  1. 1.Department of MathematicsMITCambridgeUSA
  2. 2.Department of MathematicsEPFLLausanneSwitzerland
  3. 3.Department of MathematicsUniversity of MassachusettsBostonUSA

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