One-skeleta, Betti numbers and equivariant cohomology
| dc.creator | Guillemin, Victor | |
| dc.creator | Zara, Catalin | |
| dc.date | 1999-03-09 | |
| dc.date | 2000-07-26 | |
| dc.date.accessioned | 2026-07-07T05:28:16Z | |
| dc.date.available | 2026-07-07T05:28:16Z | |
| dc.description | The one-skeleton of a G-manifold M is the set of points p in M where $\dim G_p \geq \dim G -1$; and M is a GKM manifold if the dimension of this one-skeleton is 2. Goresky, Kottwitz and MacPherson show that for such a manifold this one-skeleton has the structure of a ``labeled" graph, $(Γ, α)$, and that the equivariant cohomology ring of M is isomorphic to the ``cohomology ring'' of this graph. Hence, if M is symplectic, one can show that this ring is a free module over the symmetric algebra $\SS(\fg^*)$, with $b_{2i}(Γ)$ generators in dimension 2i, $b_{2i}(Γ)$ being the ``combinatorial'' 2i-th Betti number of $Γ$. In this article we show that this ``topological'' result is , in fact, a combinatorial result about graphs. | |
| dc.description | Revised and added content, AMSLaTex, 51 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/math/9903051 | |
| dc.identifier | http://arxiv.org/abs/math/9903051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78196 | |
| dc.subject | Differential Geometry | |
| dc.title | One-skeleta, Betti numbers and equivariant cohomology | |
| dc.type | text |