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Which circle bundles can be triangulated over $\partial \Delta^3$?

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arxiv 1807.06842 v2 pith:ONGYT24F submitted 2018-07-18 math.GT math.ATmath.CO

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classification math.GTmath.ATmath.CO
keywords bundlescircledeltapartialbaseboundarydimensionalhaving
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abstract

We proof that having boundary of standard 3-dimensional simplex $\partial \Delta^3$ as a base of triangulation one can triangulate only trivial and Hopf circle bundles.

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  1. Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle

    math.GT 2019-08 conditional novelty 7.0 of 10

    A circle bundle admits a semi-simplicial triangulation over a fixed base exactly when its Chern class has a binary 0/1 cocycle representative; on surfaces this bounds the Chern number by half the number of triangles.

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