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.

中文翻译：

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局部同调与分层

我们概述了一种算法，用于将给定的有限维正则CW复杂体的规范（或最粗糙）分层恢复为同调流形，每个流形都是单元的并集。通过迭代地将细胞的波状体定位在一个子波状体家族周围来进行构造。这些子位点又由一组共滑轮确定，该共滑轮捕获跨越基础复合体的细胞邻域的同调性变化。结果是类别的嵌套序列，每个类别都包含所有像元作为其对象集，并且具有以下性质：当且仅当两个像元位于相同的规范层中时，它们才在最后一个类别中是同构的。整个过程适合高效的分布式计算。