Morse theory on graphs
| dc.creator | Guillemin, Victor | |
| dc.creator | Zara, Catalin | |
| dc.date | 2000-07-26 | |
| dc.date.accessioned | 2026-07-07T04:36:31Z | |
| dc.date.available | 2026-07-07T04:36:31Z | |
| dc.description | Let $Γ$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $Γ$ is defined by a map, $α$, which assigns to each oriented edge e of $Γ$ a one-dimensional representation of G (or, alternatively, a weight, $α_e$, in the weight lattice of G). For the assignment, $e \to α_e$, to be a schematic description of a ``G-action'', these weights have to satisfy certain compatibility conditions: the GKM axioms. We attach to $(Γ, α)$ an equivariant cohomology ring, $H_G(Γ)=H(Γ,α)$. By definition this ring contains the equivariant cohomology ring of a point, $\SS(\fg^*) = H_G(pt)$, as a subring, and in this paper we will use graphical versions of standard Morse theoretical techniques to analyze the structure of $H_G(Γ)$ as an $\SS(\fg^*)$-module. | |
| dc.description | 23 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0007161 | |
| dc.identifier | http://arxiv.org/abs/math/0007161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59626 | |
| dc.subject | Combinatorics | |
| dc.subject | Differential Geometry | |
| dc.title | Morse theory on graphs | |
| dc.type | text |