Triangulating a Cappell-Shaneson knot complement
Ryan Budney, Benjamin A. Burton, Jonathan Hillman
TL;DR
This paper demonstrates that a Cappell-Shaneson knot complement can be triangulated with only two 4-simplices, showcasing an extremely efficient geometric decomposition.
Contribution
It provides the first known example of a Cappell-Shaneson knot complement with an extremely minimal triangulation, reducing complexity significantly.
Findings
A Cappell-Shaneson knot complement admits a triangulation with only two 4-simplices.
This minimal triangulation is the smallest known for such a manifold.
The result advances understanding of the geometric complexity of knot complements.
Abstract
We show that one of the Cappell-Shaneson knot complements admits an extraordinarily small triangulation, containing only two 4-dimensional simplices.
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