Homotopy groups of cubical sets
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908723587317760 |
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| author | Carranza, Daniel Kapulkin, Chris |
| author_facet | Carranza, Daniel Kapulkin, Chris |
| contents | We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric realization functor. We also provide purely combinatorial proofs of several classical theorems, including: product preservation, commutativity of higher homotopy groups, the long exact sequence of a fibration, and Whitehead's theorem. This is a companion paper to our "Cubical setting for discrete homotopy theory, revisited" in which we apply these results to study the homotopy theory of simple graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03511 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homotopy groups of cubical sets Carranza, Daniel Kapulkin, Chris Algebraic Topology Category Theory 55Q05, 18N40 (primary), 55U35 (secondary) We define and study homotopy groups of cubical sets. To this end, we give four definitions of homotopy groups of a cubical set, prove that they are equivalent, and further that they agree with their topological analogues via the geometric realization functor. We also provide purely combinatorial proofs of several classical theorems, including: product preservation, commutativity of higher homotopy groups, the long exact sequence of a fibration, and Whitehead's theorem. This is a companion paper to our "Cubical setting for discrete homotopy theory, revisited" in which we apply these results to study the homotopy theory of simple graphs. |
| title | Homotopy groups of cubical sets |
| topic | Algebraic Topology Category Theory 55Q05, 18N40 (primary), 55U35 (secondary) |
| url | https://arxiv.org/abs/2202.03511 |