Papers › A characterization of tightly triangulated 3-manifolds
A characterization of tightly triangulated 3-manifolds
Bhaskar Bagchi, Basudeb Datta, Jonathan Spreer
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
For a field 𝔽, the notion of 𝔽-tightness of simplicial complexes was introduced by K\"uhnel. K\"uhnel and Lutz conjectured that any 𝔽-tight triangulation of a closed manifold is the most economic of all possible triangulations of the manifold. The boundary of a triangle is the only 𝔽-tight triangulation of a closed 1-manifold. A triangulation of a closed 2-manifold is 𝔽-tight if and only if it is 𝔽-orientable and neighbourly. In this paper we prove that a triangulation of a closed 3-manifold is 𝔽-tight if and only if it is 𝔽-orientable, neighbourly and stacked. In consequence, the K\"uhnel-Lutz conjecture is valid in dimension ≤3.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections