The fundamental group and the magnitude-path spectral sequence of a directed graph

The fundamental group of a directed graph admits a natural sequence of quotient groups called \(r\)-fundamental groups, and the \(r\)-fundamental groups can capture properties of a directed graph that the fundamental group cannot capture. The fundamental group of a directed graph is related to path...

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Bibliographic Details
Published in:arXiv.org 2024-11
Main Authors: Kishimoto, Daisuke, Tong, Yichen
Format: Article
Language:English
Subjects:
Graph theory
Homology
Theorems
Online Access:Get full text
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Summary:The fundamental group of a directed graph admits a natural sequence of quotient groups called \(r\)-fundamental groups, and the \(r\)-fundamental groups can capture properties of a directed graph that the fundamental group cannot capture. The fundamental group of a directed graph is related to path homology through the Hurewicz theorem. The magnitude-path spectral sequence connects magnitude homology and path homology of a directed graph, and it may be thought of as a sequence of homology of a directed graph, including path homology. In this paper, we study relations of the \(r\)-fundamental groups and the magnitude-path spectral sequence through the Hurewicz theorem and the Seifert-van Kampen theorem.
ISSN:2331-8422