论文标题
Hochschild同源性，以及通过连接挖掘的持续方法
Hochschild homology, and a persistent approach via connectivity digraphs
论文作者
论文摘要
我们引入了一个持久的Hochschild同源框架，用于有向图。 Hochschild同源组（路径代数）指示图消失在$ i \ geq 2 $中。为了将它们扩展到更高的程度，我们介绍了连通性挖掘的概念，并分析了两个主要示例。第一个是由Atkin的$ Q $ - 连接性引起的，第二个是在这里称为$ n $ path Digraphs，从而概括了线图的经典概念。基于持续同源性的分类环境，我们提出了一条稳定的管道来计算持续的Hochschild同源组。该管道也适合其他同源理论。因此，我们通过一项关于Digraphs同源性理论的调查来补充我们的工作。
We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digraphs and analyse two main examples; the first, arising from Atkin's $q$-connectivity, and the second, here called $n$-path digraphs, generalising the classical notion of line graphs. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable to other homology theories; for this reason, we complement our work with a survey on homology theories of digraphs.
