论文标题
具有不可裁定的轨道空间的矩角歧管的概括
A generalization of moment-angle manifolds with non-contractible orbit spaces
论文作者
论文摘要
我们将矩角歧管的概念概括为简单的凸多物质，以与角落的任意良好歧管。 For a nice manifold with corners Q, we first compute the stable decomposition of the moment-angle manifold Z_Q via a construction called rim-cubicalization of Q. From this, we derive a formula to compute the integral cohomology group of Z_Q via the strata of Q. This generalizes the Hochster's formula for the moment-angle manifold over a simple convex polytope.此外，我们使用部分对角线图的想法获得了Z_Q的积分共同体学环的描述。此外，我们在Q上定义了一系列基于CW-复合物的序列的多面体产物的概念，并获得了这些空间的类似结果，就像我们对Z_Q所做的一样。使用这种一般结构，我们可以根据Q的davis-Januszkiewicz的规范圆环的作用来计算ZQ的模棱两可的共同体学环。该结果将导致Q的新概念的定义，称为Q的拓扑表环，这概括了简单的多层镜头的脸环的概念。同时，我们在Q上获得了真实的矩角RZ_Q的一些并行结果。
We generalize the notion of moment-angle manifold over a simple convex polytope to an arbitrary nice manifold with corners. For a nice manifold with corners Q, we first compute the stable decomposition of the moment-angle manifold Z_Q via a construction called rim-cubicalization of Q. From this, we derive a formula to compute the integral cohomology group of Z_Q via the strata of Q. This generalizes the Hochster's formula for the moment-angle manifold over a simple convex polytope. Moreover, we obtain a description of the integral cohomology ring of Z_Q using the idea of partial diagonal maps. In addition, we define the notion of polyhedral product of a sequence of based CW-complexes over Q and obtain similar results for these spaces as we do for Z_Q. Using this general construction, we can compute the equivariant cohomology ring of Z_Q with respect to its canonical torus action from the Davis-Januszkiewicz space of Q. The result leads to the definition of a new notion called the topological face ring of Q, which generalizes the notion of face ring of a simple polytope. Meanwhile, we obtain some parallel results for the real moment-angle manifold RZ_Q over Q.
