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- W4295266407 abstract "Let $T$ be a compact torus and $X$ be a a finite $T$-CW complex (e.g. a compact $T$-manifold). In earlier work, the second author introduced a functor which assigns to $X$ a so called GKM-sheaf $mathcal{F}_X$ whose ring of global sections $H^0(mathcal{F}_X)$ is isomorphic to the equivariant cohomology $H^*_T(X)$ whenever $X$ is equivariantly formal (meaning that $H^*_T(X)$ is a free module over $H^*(BT))$. In the current paper we prove more generally that $H^0(mathcal{F}_X) cong H^*_T(X)$ if and only if $H_T^*(X)$ is reflexive, and find a geometric interpretation of the higher cohomology $H^n(mathcal{F}_X)$ for $n geq 1$." @default.
- W4295266407 created "2022-09-12" @default.
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- W4295266407 date "2018-06-05" @default.
- W4295266407 modified "2023-09-24" @default.
- W4295266407 title "Cohomology of GKM-sheaves" @default.
- W4295266407 doi "https://doi.org/10.48550/arxiv.1806.01761" @default.
- W4295266407 hasPublicationYear "2018" @default.
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