Equivariant cohomology distinguishes toric manifolds
Equivariant cohomology distinguishes toric manifolds
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DOI：
10.1016/j.aim.2008.04.002
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发表时间：
2007-03
影响因子：
1.7
通讯作者：
M. Masuda
中科院分区：
文献类型：
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作者：
M. Masuda
具有群作用的空间的等变上同调不仅是环，而且是作用群的分类空间的上同调环上的代数。证明了环面流形(即紧致光滑环面簇)与簇同构的充要条件是它们的等变上同调代数是弱同构的。我们还证明了可以被认为是环面流形的拓扑对应的拟流形是等价同胚当且仅当它们的等变上同调代数是同构的。
The equivariant cohomology of a space with a group action is not only a ring but also an algebra over the cohomology ring of the classifying space of the acting group. We prove that toric manifolds (i.e. compact smooth toric varieties) are isomorphic as varieties if and only if their equivariant cohomology algebras are weakly isomorphic. We also prove that quasitoric manifolds, which can be thought of as a topological counterpart to toric manifolds, are equivariantly homeomorphic if and only if their equivariant cohomology algebras are isomorphic.