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