论文标题
分区综合体：组合交换代数的邀请
The Partition Complex: an invitation to combinatorial commutative algebra
论文作者
论文摘要
我们使用[ADI18]中引入的分区综合体为组合交换代数和斯坦利 - 赖斯纳理论提供了新的基础。主要优点之一是，它仅使用对代数和拓扑的知识，完全是独立的。另一方面，我们还使用这种方法开发了新技术和结果。特别是我们提供 - 一种新颖的独立方法，是建立Reisner定理和Schenzel的Buchsbaum Complexse的公式。 - 一种简单的新方法，比以前的治疗方法更具一般性和精度来建立庞加莱二元性。 - 一个“主理论”，概括了有关Lefschetz定理的几个先前结果。 - 证明了库赫内尔关于边界三角歧管的猜想。
We provide a new foundation for combinatorial commutative algebra and Stanley-Reisner theory using the partition complex introduced in [Adi18]. One of the main advantages is that it is entirely self-contained, using only a minimal knowledge of algebra and topology. On the other hand, we also develop new techniques and results using this approach. In particular, we provide - A novel, self-contained method of establishing Reisner's theorem and Schenzel's formula for Buchsbaum complexes. - A simple new way to establish Poincaré duality for face rings of manifolds, in much greater generality and precision than previous treatments. - A "master-theorem" to generalize several previous results concerning the Lefschetz theorem on subdivisions. - Proof for a conjecture of Kühnel concerning triangulated manifolds with boundary.
