Mapping fiber, loop and suspension graphs in naive discrete homotopy theory
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913741344342016 |
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| author | Yamagata, So |
| author_facet | Yamagata, So |
| contents | Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the (non-)similarities between the A-homotopy and ordinary homotopy theories through explicit constructions. More precisely, we define mapping fiber graphs and study their basic properties yielding, under a technical condition, a discrete analogous of Puppe sequence in a naive discrete homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15714 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mapping fiber, loop and suspension graphs in naive discrete homotopy theory Yamagata, So Combinatorics Algebraic Topology 05C25, 55P10 Discrete homotopy theory or A-homotopy theory is a combinatorial homotopy theory defined on graphs, simplicial complexes, and metric spaces, reflecting information about their connectivity. The present paper aims to further understand the (non-)similarities between the A-homotopy and ordinary homotopy theories through explicit constructions. More precisely, we define mapping fiber graphs and study their basic properties yielding, under a technical condition, a discrete analogous of Puppe sequence in a naive discrete homotopy theory. |
| title | Mapping fiber, loop and suspension graphs in naive discrete homotopy theory |
| topic | Combinatorics Algebraic Topology 05C25, 55P10 |
| url | https://arxiv.org/abs/2402.15714 |