Homotopy Groups and Puppe Sequence of Digraphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909600249282560 |
|---|---|
| author | Li, Jingyan Wu, Jie Yau, Shing-Tung Zhang, Mengmeng |
| author_facet | Li, Jingyan Wu, Jie Yau, Shing-Tung Zhang, Mengmeng |
| contents | We introduce homotopy groups of digraphs that admit an intuitive description of grid structures, which is a variation of the GLMY homotopy groups introduced by Grigor'yan, Lin, Muranov and Yau in 2014. This direct approach enables a descriptive interpretation of GLMY theory in applications such as network science. Furthermore, we prove that there exists a long exact sequence of homotopy groups of digraphs associated to any based digraph map, that is, there exists a digraph version of the Puppe sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Homotopy Groups and Puppe Sequence of Digraphs Li, Jingyan Wu, Jie Yau, Shing-Tung Zhang, Mengmeng Algebraic Topology 55Q05 (Primary), 55R65 (Secondary) We introduce homotopy groups of digraphs that admit an intuitive description of grid structures, which is a variation of the GLMY homotopy groups introduced by Grigor'yan, Lin, Muranov and Yau in 2014. This direct approach enables a descriptive interpretation of GLMY theory in applications such as network science. Furthermore, we prove that there exists a long exact sequence of homotopy groups of digraphs associated to any based digraph map, that is, there exists a digraph version of the Puppe sequence. |
| title | Homotopy Groups and Puppe Sequence of Digraphs |
| topic | Algebraic Topology 55Q05 (Primary), 55R65 (Secondary) |
| url | https://arxiv.org/abs/2402.01110 |