A characterization of tightly triangulated 3-manifolds
European Journal of Combinatorics
For a field F, the notion of F-tightness of simplicial complexes was introduced by Kühnel. Kühnel and Lutz conjectured that F-tight triangulations of a closed manifold are 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 Kühnel–Lutz conjecture is valid in dimension ≤3.
Bagchi, Bhaskar; Datta, Basudeb; and Spreer, Jonathan, "A characterization of tightly triangulated 3-manifolds" (2017). Journal Articles. 2671.