Geodesic
A GKM description of the equivariant cohomology ring of a homogeneous space
Journal of Algebraic Combinatorics, Tome 23 (2006) no. 1, pp. 21-41.

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Summary: 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.
Mots-clés : keywords GKM graph, homogeneous spaces, equivariant cohomology 
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     title = {A {GKM} description of the equivariant cohomology ring of a homogeneous space},
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Guillemin, V.; Holm, T.; Zara, C. A GKM description of the equivariant cohomology ring of a homogeneous space. Journal of Algebraic Combinatorics, Tome 23 (2006) no. 1, pp. 21-41. https://geodesic-test.mathdoc.fr/item/JAC_2006__23_1_a3/