A GKM description of the equivariant cohomology ring of a homogeneous space
| dc.creator | Guillemin, Victor | |
| dc.creator | Holm, Tara | |
| dc.creator | Zara, Catalin | |
| dc.date | 2001-12-18 | |
| dc.date.accessioned | 2026-07-07T04:45:19Z | |
| dc.date.available | 2026-07-07T04:45:19Z | |
| dc.description | 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 \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.description | 19 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0112184 | |
| dc.identifier | http://arxiv.org/abs/math/0112184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62910 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 53D05 (Primary); 55N91; 05C25 (Secondary) | |
| dc.title | A GKM description of the equivariant cohomology ring of a homogeneous space | |
| dc.type | text |