Which circle bundles can be triangulated over $\partial \Delta^3$?
N. Mn\"ev
TL;DR
This paper proves that only trivial and Hopf circle bundles can be triangulated over the boundary of a 3-simplex, providing a classification of such triangulations.
Contribution
It establishes a classification result showing that only trivial and Hopf circle bundles admit triangulations over boundary of the 3-simplex.
Findings
Only trivial circle bundles can be triangulated over boundary.
Hopf circle bundles are also triangulable over this boundary.
No other circle bundles admit such triangulations.
Abstract
We proof that having boundary of standard 3-dimensional simplex as a base of triangulation one can triangulate only trivial and Hopf circle bundles.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology