$K(Z,2)$ out of circular permutations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916360331722752 |
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| author | Mnëv, Nikolai |
| author_facet | Mnëv, Nikolai |
| contents | We discuss $\pmb{SC}_*$, a simplicial homotopy model of $K(Z,2)$ constructed from circular permutations. In any dimension, the number of simplices in the model is finite. The complex $\pmb{SC}_*$ naturally manifests as a simplicial set representing ``minimally" triangulated circle bundles over simplicial bases. On the other hand, existence of the homotopy equivalence $|\pmb{SC}_*| \approx B(U(1)) \approx K(Z,2)$ appears to be a canonical fact from the foundations of the theory of crossed simplicial groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01625 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $K(Z,2)$ out of circular permutations Mnëv, Nikolai Algebraic Topology Combinatorics We discuss $\pmb{SC}_*$, a simplicial homotopy model of $K(Z,2)$ constructed from circular permutations. In any dimension, the number of simplices in the model is finite. The complex $\pmb{SC}_*$ naturally manifests as a simplicial set representing ``minimally" triangulated circle bundles over simplicial bases. On the other hand, existence of the homotopy equivalence $|\pmb{SC}_*| \approx B(U(1)) \approx K(Z,2)$ appears to be a canonical fact from the foundations of the theory of crossed simplicial groups. |
| title | $K(Z,2)$ out of circular permutations |
| topic | Algebraic Topology Combinatorics |
| url | https://arxiv.org/abs/2406.01625 |