Local Cohomology and Stratification
Local Cohomology and Stratification
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局部上同调和分层
DOI：
10.1007/s10208-019-09424-0
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发表时间：
2017
影响因子：
3
通讯作者：
Vidit Nanda
中科院分区：
文献类型：
--
作者：
Vidit Nanda
我们概述了一个算法来恢复规范（或，粗）分层的一个给定的有限维规则CW复杂的上同调流形，其中每个是一个工会的细胞。通过迭代地将细胞的偏序集局部化到一个子集族来进行构建;这些子集又由一组共层来确定，这些共层捕获了整个基础复合体中细胞邻域的上同调变化。结果是一个嵌套的范畴序列，每个范畴包含所有的细胞作为其对象集，具有两个细胞在最后一个范畴中同构的性质，当且仅当它们位于同一个规范层中。整个过程是服从高效的分布式计算。
We outline an algorithm to recover the canonical (or, coarsest) stratification of a given finite-dimensional regular CW complex into cohomology manifolds, each of which is a union of cells. The construction proceeds by iteratively localizing the poset of cells about a family of subposets; these subposets are in turn determined by a collection of cosheaves which capture variations in cohomology of cellular neighborhoods across the underlying complex. The result is a nested sequence of categories, each containing all the cells as its set of objects, with the property that two cells are isomorphic in the last category if and only if they lie in the same canonical stratum. The entire process is amenable to efficient distributed computation.