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- W2952697629 abstract "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, $(Gamma, alpha)$, 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 $b_{2i}(Gamma)$ generators in dimension 2i, $b_{2i}(Gamma)$ being the ``combinatorial'' 2i-th Betti number of $Gamma$. In this article we show that this ``topological'' result is , in fact, a combinatorial result about graphs." @default.
- W2952697629 created "2019-06-27" @default.
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- W2952697629 date "1999-03-09" @default.
- W2952697629 modified "2023-09-27" @default.
- W2952697629 title "One-skeleta, Betti numbers and equivariant cohomology" @default.
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