部分有序集合的格同调

Pub Date : 2024-07-24 DOI:10.1556/012.2024.04312

Tamás Ágoston, András Némethi

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引用次数: 0

摘要

在本文中，我们介绍了一种加权 CW 复数（以及相关的格同调）的构造，它对应于具有某些附加结构的部分有序集合。这是对[4]中的构造的推广，在[4]中，我们从给定向量空间的子空间系统出发。我们接下来要证明这种构造的一些基本性质，这些性质在许多方面都与子空间情况下的性质类似，但构造的某些方面导致了这种情况下所不存在的复杂性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Lattice Cohomology of Partially Ordered Sets

In this paper we introduce a construction for a weighted CW complex (and the associated lattice cohomology) corresponding to partially ordered sets with some additional structure. This is a generalization of the construction seen in [4] where we started from a system of subspaces of a given vector space. We then proceed to prove some basic properties of this construction that are in many ways analogous to those seen in the case of subspaces, but some aspects of the construction result in complexities not present in that scenario.

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