Calculating Higher Digraph Homotopy Groups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913778168233984 |
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| author | Theriault, Stephen Wu, Jie Yau, Shing-Tung Zhang, Mengmeng |
| author_facet | Theriault, Stephen Wu, Jie Yau, Shing-Tung Zhang, Mengmeng |
| contents | We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this we define relative digraph homotopy groups and show these satisfy a long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Calculating Higher Digraph Homotopy Groups Theriault, Stephen Wu, Jie Yau, Shing-Tung Zhang, Mengmeng Algebraic Topology 05C20, 55Q05 We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this we define relative digraph homotopy groups and show these satisfy a long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs. |
| title | Calculating Higher Digraph Homotopy Groups |
| topic | Algebraic Topology 05C20, 55Q05 |
| url | https://arxiv.org/abs/2504.04119 |