We investigate a PL topology question: which circle bundles can be triangulated over a given triangulation of the base? The question gets 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: the classical Huntington transitivity axiom for cyclic orders can be expressed as the universal binary Chern cocycle.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 481, 2019, pp. 87–107.
Research is supported by the Russian Science Foundation grant 19-71-30002.
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Mnëv, N. Minimal Triangulations of Circle Bundles, Circular Permutations, and the Binary Chern Cocycle. J Math Sci 247, 696–710 (2020). https://doi.org/10.1007/s10958-020-04832-y
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DOI: https://doi.org/10.1007/s10958-020-04832-y