有序空间的同源数图

Pub Date : 2024-07-27 DOI:10.1007/s40062-024-00352-7

Catarina Faustino, Thomas Kahl

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引用次数: 0

摘要

本文研究有序空间的有向同调概念，即同调数字图。我们证明了同调数字图是有向同调不变式，并为同调数字图建立了普通奇异同调理论主要结果的变体。特别是，我们证明了一个库奈特公式，通过这个公式，我们可以从各部分的同调数字图计算出预序空间乘积的同调数字图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

The homology digraph of a preordered space

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The homology digraph of a preordered space

This paper studies a notion of directed homology for preordered spaces, called the homology digraph. We show that the homology digraph is a directed homotopy invariant and establish variants of the main results of ordinary singular homology theory for the homology digraph. In particular, we prove a Künneth formula, which enables one to compute the homology digraph of a product of preordered spaces from the homology digraphs of the components.

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