Morse theory on graphs

Details Morse theory on graphs Morse theory on graphs

2000-07-26

arxiv.org/abs/math/0007161v1

Mathematics

Combinatorics

23 pages, 1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Morse theory on graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Morse theory on graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Morse theory on graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-582507