有向图的可达性同调
代数拓扑
2025-03-27 v3 组合数学
范畴论
摘要
过去十年见证了道路同调和幅度同调的发展——这是有向图的两种同调理论，各自满足 Kunneth 和 Mayer-Vietoris 定理等经典性质。Asao 最近的工作表明，幅度同调和道路同调是相关的，它们出现在某一谱序列的不同页上。这里我们研究该谱序列的目标，我们称之为可达性同调。我们证明了它满足适当的同伦不变性、Kunneth 定理、切除定理和 Mayer-Vietoris 定理，这些性质均比幅度同调或道路同调中相应的性质更强。
引用
@article{arxiv.2312.01378,
title = {The reachability homology of a directed graph},
author = {Richard Hepworth and Emily Roff},
journal= {arXiv preprint arXiv:2312.01378},
year = {2025}
}
备注
20 pages. Version 2: acknowledgements and references updated; a few typos corrected; minor improvements to the exposition. Version 3: references updated. This is the final version, published in International Mathematics Research Notices