The reachability homology of a directed graph
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910893641564160 |
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| author | Hepworth, Richard Roff, Emily |
| author_facet | Hepworth, Richard Roff, Emily |
| contents | The last decade has seen the development of path homology and magnitude homology -- two homology theories of directed graphs, each satisfying classic properties such as Kunneth and Mayer-Vietoris theorems. Recent work of Asao has shown that magnitude homology and path homology are related, appearing in different pages of a certain spectral sequence. Here we study the target of that spectral sequence, which we call reachability homology. We prove that it satisfies appropriate homotopy invariance, Kunneth, excision, and Mayer-Vietoris theorems, these all being stronger than the corresponding properties for either magnitude or path homology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01378 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The reachability homology of a directed graph Hepworth, Richard Roff, Emily Algebraic Topology Combinatorics Category Theory 18G90, 05C25 (Primary) 05C31, 05C38, 18G35 (Secondary) The last decade has seen the development of path homology and magnitude homology -- two homology theories of directed graphs, each satisfying classic properties such as Kunneth and Mayer-Vietoris theorems. Recent work of Asao has shown that magnitude homology and path homology are related, appearing in different pages of a certain spectral sequence. Here we study the target of that spectral sequence, which we call reachability homology. We prove that it satisfies appropriate homotopy invariance, Kunneth, excision, and Mayer-Vietoris theorems, these all being stronger than the corresponding properties for either magnitude or path homology. |
| title | The reachability homology of a directed graph |
| topic | Algebraic Topology Combinatorics Category Theory 18G90, 05C25 (Primary) 05C31, 05C38, 18G35 (Secondary) |
| url | https://arxiv.org/abs/2312.01378 |