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

Nikolai Mnëv

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

Algebraic Topology 2024-08-20 v2 Combinatorics

Authors: Nikolai Mnëv

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.

Keywords

simplicial homotopy K(Z,2) circular permutations crossed simplicial groups circle bundles triangulation

Cite

@article{arxiv.2406.01625,
  title  = {$K(Z,2)$ out of circular permutations},
  author = {Nikolai Mnëv},
  journal= {arXiv preprint arXiv:2406.01625},
  year   = {2024}
}

Comments

24 pages, major update on proof of previously announced theorem

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

Abstract

Keywords

Cite

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