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arXiv · 2406.01625

$K(Z,2)$ out of circular permutations

Nikolai Mnëv
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Abstract

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.

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Nikolai Mnëv. 2024-06-01. $K(Z,2)$ out of circular permutations. https://arxiv.org/abs/2406.01625

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