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- W1531625674 abstract "Let $Gamma$ be a finite d-valent graph and G an n-dimensional torus. An ``action'' of G on $Gamma$ is defined by a map, $alpha$, which assigns to each oriented edge e of $Gamma$ a one-dimensional representation of G (or, alternatively, a weight, $alpha_e$, in the weight lattice of G). For the assignment, $e to alpha_e$, to be a schematic description of a ``G-action'', these weights have to satisfy certain compatibility conditions: the GKM axioms. We attach to $(Gamma, alpha)$ an equivariant cohomology ring, $H_G(Gamma)=H(Gamma,alpha)$. 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 $H_G(Gamma)$ as an $SS(fg^*)$-module." @default.
- W1531625674 created "2016-06-24" @default.
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- W1531625674 date "2000-07-26" @default.
- W1531625674 modified "2023-09-27" @default.
- W1531625674 title "Morse theory on graphs" @default.
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