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.
Which circle bundles can be triangulated over $\partial \Delta^3$?
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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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math.GT 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Minimal triangulations of circle bundles, circular permutations and binary Chern cocycle
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.