论文标题
关于矩角复合物及其应用的同质分解
On the homotopy decomposition for the quotient of a moment-angle complex and its applications
论文作者
论文摘要
在本文中，我们证明，在其上自然作用的紧凑型圆环中任何封闭的亚组的实际或复杂的矩角复合物的商都是同等的，等于同型圆锥形图的同质性。对于任何商，我们都证明了同构的同态性，概括了众所周知的戴维斯 - 贾努斯兹基维奇（Davis-Januszkiewicz）的构造，用于准确的歧管和小型封面。在复杂情况下，我们在自然假设下推断了相应的鲍尔建筑空间的形式，从而导致任何坐标亚组对商的新闻的新描述。我们证明了对角圆作用的任何部分商的弱质量猜想。我们通过在整体共同体中具有任意扭转的圈子动作来明确构造部分商。
In this paper we prove that the quotient of any real or complex moment-angle complex by any closed subgroup in the naturally acting compact torus on it is equivariantly homotopy equivalent to the homotopy colimit of a certain toric diagram. For any quotient we prove an equivariant homeomorphism generalizing the well-known Davis-Januszkiewicz construction for quasitoric manifolds and small covers. We deduce formality of the corresponding Borel construction space under the natural assumption on the group action in the complex case leading to the new description of the equivariant cohomology for the quotients by any coordinate subgroups. We prove the weak Toral Rank Conjecture for any partial quotient by the diagonal circle action. We give an explicit construction of partial quotients by circle actions having arbitrary torsion in integral cohomology.
