论文标题
从其模棱两可的共同体中重建圆环动作的轨道类型分层
Reconstructing the orbit type stratification of a torus action from its equivariant cohomology
论文作者
论文摘要
我们研究了关于紧凑空间的圆环作用轨道类型分层的哪些信息包含在其理性的同学代数中。关于分层的（标记的）POSET结构，我们表明地位同胞编码了分支元素的子库。为了进行等效的正式行动，我们还研究了分层的共同体学信息。在平滑的环境中，我们表明，在某些条件下 - 特别适合具有离散固定点集的紧凑定向歧管 - 地层的均等共同体编码是在歧管的模棱两可的同居中。
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.
