A Construction Principle for Tight and Minimal Triangulations of Manifolds
Benjamin A. Burton, Basudeb Datta, Nitin Kumar Singh, Jonathan Spreer · NOT FOUND REPOSITORY (Indian Institute of Science Bangalore) · 2018
Tight triangulations are exotic, but highly regular objects in combinatorial topology. A triangulation is tight if all its piecewise linear embeddings into a Euclidean space are as convex as allowed by the topology of the underlying manifold. Tight triangulations are conjectured to be stronglyminimal and proven to be so for dimensions = 2. While we still do not know if there are infinitely many tight triangulations in a fixed dimension d > 2, this result shows that there are abundantly many.