Cubical setting for discrete homotopy theory, revisited
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917158227804160 |
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| author | Carranza, Daniel Kapulkin, Chris |
| author_facet | Carranza, Daniel Kapulkin, Chris |
| contents | We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use this to prove a conjecture of Babson, Barcelo, de Longueville, and Laubenbacher from 2006, and a strong version of the Hurewicz theorem in discrete homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03516 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cubical setting for discrete homotopy theory, revisited Carranza, Daniel Kapulkin, Chris Combinatorics Algebraic Topology Category Theory 05C25, 55U35 (primary), 18N40, 18N45 (secondary) We construct a functor associating a cubical set to a (simple) graph. We show that cubical sets arising in this way are Kan complexes, and that the A-groups of a graph coincide with the homotopy groups of the associated Kan complex. We use this to prove a conjecture of Babson, Barcelo, de Longueville, and Laubenbacher from 2006, and a strong version of the Hurewicz theorem in discrete homotopy theory. |
| title | Cubical setting for discrete homotopy theory, revisited |
| topic | Combinatorics Algebraic Topology Category Theory 05C25, 55U35 (primary), 18N40, 18N45 (secondary) |
| url | https://arxiv.org/abs/2202.03516 |