Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle
arXiv:1908.04029
Abstract
We investigate a PL topology question: which circle bundles can be triangulated over a given triangulation of the base? The question got a simple answer emphasizing the role of minimal triangulations encoded by local systems of circular permutations of vertices of the base simplices. The answer is based on an experimental fact: classical Huntington transitivity axiom for cyclic orders can be expressed as the universal binary Chern cocycle.
21 pages, language corrections