K(Z,2) out of circular permutations

2024/06/01 by Mnëv, Nikolai
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2406.01625

Abstract

We discuss \pmbSC_*, 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 \pmbSC_* naturally manifests as a simplicial set representing ``minimally" triangulated circle bundles over simplicial bases. On the other hand, existence of the homotopy equivalence |\pmbSC_*| ≈ B(U(1)) ≈ K(Z,2) appears to be a canonical fact from the foundations of the theory of crossed simplicial groups.

Related

• Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle
• Minimal fibrations and the organizing theorem of simplicial homotopy theory
• Topology of scrambled simplices
• Universal simplicial complexes inspired by toric topology
• Homotopy Theory for Ordered Simplicial Complexes