By Kuhnel W., Lutz F. H.
A triangulation of a manifold (or pseudomanifold) is termed a decent triangulation if any simplexwise linear embedding into any Euclidean area is tight. Tightness of an embedding signifies that the inclusion of any sublevel chosen by means of a linear practical is injective in homology and, consequently, topologically crucial. Tightness is a generalization of convexity, and the tightness of a triangulation is a reasonably restrictive estate. We supply a overview on all recognized examples of tight triangulations and formulate a (computer-aided) enumeration theorem for the case of at such a lot 15 vertices and the presence of a vertex-transitive automorphism workforce. Altogether, six new examples of tight triangulations are offered, a vertex-transitive triangulation of the easily attached homogeneous 5-manifold SU(3)/SO(3) with vertex-transitive motion, non-symmetric 12-vertex triangulations of , and non-symmetric triangulations of on thirteen vertices.
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A Census of Tight Triangulations by Kuhnel W., Lutz F. H.