Abstract:
We discuss $SC_*$, a simplicial homotopy model of $K(\mathbb{Z},2)$ 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 $|SC_*| \approx B(U(1)) \approx K(\mathbb{Z},2)$ appears to be a canonical fact from the foundations of the theory of crossed simplicial groups.
Key words and phrases:circle bundles, circular permutations, crossed simplicial groups.
Fulltext:
PDF file (555 kB)