The homology digraph of a preordered space

Catarina Faustino; Thomas Kahl

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arXiv · 2312.02676

The homology digraph of a preordered space

Catarina Faustino·Thomas Kahl

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Abstract

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 K\"unneth 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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Catarina Faustino, Thomas Kahl. 2023-12-05. The homology digraph of a preordered space. https://arxiv.org/abs/2312.02676

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