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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 481, Pages 87–107 (Mi znsl6780)  
Minimal triangulations of circle bundles, circular permutations, and the binary Chern cocycle

N. Mnëvab

a Chebyshev Laboratory, St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Institute of Mathematics, St. Petersburg, Russia
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Abstract: 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.
Key words and phrases: bundle triangulations, Chern class.
Funding agency Grant number
Russian Science Foundation 19-71-30002
Research is supported by the Russian Science Foundation grant 19-71-30002.
Received: 10.09.2019
Document Type: Article
UDC: 515.145.25, 515.145.82
Language: English
Citation: N. Mnëv, “Minimal triangulations of circle bundles, circular permutations, and the binary Chern cocycle”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXX, Zap. Nauchn. Sem. POMI, 481, POMI, St. Petersburg, 2019, 87–107
Citation in format AMSBIB
\Bibitem{Mne19}
\by N.~Mn\"ev
\paper Minimal triangulations of circle bundles, circular permutations, and the binary Chern cocycle
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XXX
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 481
\pages 87--107
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6780}
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