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首页> 外文期刊>Journal of algebraic combinatorics >Reconstructing the orbit type stratification of a torus action from its equivariant cohomology
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Reconstructing the orbit type stratification of a torus action from its equivariant cohomology

机译:Reconstructing the orbit type stratification of a torus action from its equivariant cohomology

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摘要

We investigate what information on the orbit type stratification of a torus action on a compact space is contained in its rational equivariant cohomology algebra. Regarding the (labelled) poset structure of the stratification, we show that equivariant cohomology encodes the subposet of ramified elements. For equivariantly formal actions, we also examine what cohomological information of the stratification is encoded. In the smooth setting, we show that under certain conditions-which in particular hold for a compact orientable manifold with discrete fixed point set-the equivariant cohomologies of the strata are encoded in the equivariant cohomology of the manifold.

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