论文标题
模棱两可的共同体学和有条件的矩形
Equivariant cohomology and conditional oriented matroids
论文作者
论文摘要
我们对$（\ Mathcal {a}，\ Mathcal {k}）$的varchenko- gelfand环上的重物滤清器进行了共同解释，其中$ \ mathcal {a} $是一个真正的增生平面布置，而$ \ \ m nathcal {k} $是一个conve subset convex sebset。这是基于第一作者的工作，他从纯粹的代数角度研究了过滤，以及莫斯利的作品，在特殊情况下，他在$ \ mathcal {k} $的特殊情况下进行了共同的解释。我们还定义了条件定向的矩阵的gelfand-rybnikov环，同时概括了gelfand- rybnikov rybnikov ring a rybnikov ring of方向的矩阵和上述的varchenko- gerefanko-gerefand-glchenko--我们纯粹对环，其相关分级及其REES代数进行纯粹的组合演示。
We give a cohomological interpretation of the Heaviside filtration on the Varchenko--Gelfand ring of a pair $(\mathcal{A},\mathcal{K})$, where $\mathcal{A}$ is a real hyperplane arrangement and $\mathcal{K}$ is a convex open subset of the ambient vector space. This builds on work of the first author, who studied the filtration from a purely algebraic perspective, as well as work of Moseley, who gave a cohomological interpretation in the special case where $\mathcal{K}$ is the ambient vector space. We also define the Gelfand--Rybnikov ring of a conditional oriented matroid, which simultaneously generalizes the Gelfand--Rybnikov ring of an oriented matroid and the aforementioned Varchenko--Gelfand ring of a pair. We give purely combinatorial presentations of the ring, its associated graded, and its Rees algebra.
