Eulerian magnitude homology: diagonality, injective words, and regular path homology
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916918846291968 |
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| author | Caputi, Luigi Menara, Giuliamaria |
| author_facet | Caputi, Luigi Menara, Giuliamaria |
| contents | In this paper we explore the algebraic structure and combinatorial properties of eulerian magnitude homology. First, we analyze the diagonality conditions of eulerian magnitude homology, providing a characterization of complete graphs. Then, we construct the regular magnitude-path spectral sequence as the spectral sequence of the (filtered) injective nerve of the reachability category, and explore its consequences. Among others, we show that such spectral sequence converges to the complex of injective words on a digraph, and yields characterization results for the regular path homology of diagonal directed graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_06722 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Eulerian magnitude homology: diagonality, injective words, and regular path homology Caputi, Luigi Menara, Giuliamaria Combinatorics Algebraic Topology Category Theory In this paper we explore the algebraic structure and combinatorial properties of eulerian magnitude homology. First, we analyze the diagonality conditions of eulerian magnitude homology, providing a characterization of complete graphs. Then, we construct the regular magnitude-path spectral sequence as the spectral sequence of the (filtered) injective nerve of the reachability category, and explore its consequences. Among others, we show that such spectral sequence converges to the complex of injective words on a digraph, and yields characterization results for the regular path homology of diagonal directed graphs. |
| title | Eulerian magnitude homology: diagonality, injective words, and regular path homology |
| topic | Combinatorics Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2503.06722 |