A characterization of tightly triangulated 3-manifolds. (March 2017) - Bagchi, Bhaskar; Datta, Basudeb; Spreer, Jonathan
Abstract: 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 .