有向超图的路径同调

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-09-20 DOI:10.4310/hha.2022.v24.n2.a18

Y. Muranov, A. Szczepkowska, V. Vershinin

引用次数: 2

摘要

我们描述了为有向超图构造的各种路径同调理论。我们引入了有向超图的范畴和这个范畴中的同伦图的概念。此外，我们还研究了引入的路径同调群的函数性和同态不变性。我们提供了计算这些同调群的例子。

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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Path homology of directed hypergraphs

We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy invariance of the introduced path homology groups. We provide examples of computation of these homology groups.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.