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

dc.creatorGuillemin, Victor
dc.creatorHolm, Tara
dc.creatorZara, Catalin
dc.date2001-12-18
dc.date.accessioned2026-07-07T04:45:19Z
dc.date.available2026-07-07T04:45:19Z
dc.descriptionLet $T$ 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 \emph{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.
dc.description19 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0112184
dc.identifierhttp://arxiv.org/abs/math/0112184
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62910
dc.subjectSymplectic Geometry
dc.subjectCombinatorics
dc.subject53D05 (Primary); 55N91; 05C25 (Secondary)
dc.titleA GKM description of the equivariant cohomology ring of a homogeneous space
dc.typetext

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