Journal of Algebraic Combinatorics

, Volume 23, Issue 1, pp 21–41 | Cite as

A GKM description of the equivariant cohomology ring of a homogeneous space

  • V. Guillemin
  • T. Holm
  • C. Zara


Let T be a torus of dimension n > 1 and M a compact T-manifold. M is a GKM manifold if the set of zero dimensional orbits in the orbit space M/T is zero dimensional and the set of one dimensional orbits in M/T is one dimensional. For such a manifold these sets of orbits have the structure of a labelled graph and it is known that a lot of topological information about M is encoded in this graph.

In this paper we prove that every compact homogeneous space M of non-zero Euler characteristic is of GKM type and show that the graph associated with M encodes geometric information about M as well as topological information. For example, from this graph one can detect whether M admits an invariant complex structure or an invariant almost complex structure.


GKM graph Homogeneous spaces Equivariant cohomology 


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsMITCambridge
  2. 2.Department of MathematicsUniversity of Connecticut
  3. 3.Department of MathematicsPenn State Altoona

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