The fundamental group and the magnitude-path spectral sequence of a directed graph
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912388611047424 |
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| author | Kishimoto, Daisuke Tong, Yichen |
| author_facet | Kishimoto, Daisuke Tong, Yichen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_02838 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The fundamental group and the magnitude-path spectral sequence of a directed graph Kishimoto, Daisuke Tong, Yichen Algebraic Topology Combinatorics 05C20, 55Q70 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. |
| title | The fundamental group and the magnitude-path spectral sequence of a directed graph |
| topic | Algebraic Topology Combinatorics 05C20, 55Q70 |
| url | https://arxiv.org/abs/2411.02838 |