ISSN:
1588-2829
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A triangulation of a manifold (or pseudomanifold) is called a tight triangulation if any simplexwise linear embedding into any Euclidean space is tight. Tightness of an embedding means that the inclusion of any sublevel selected by a linear functional is injective in homology and, therefore, topologically essential. Tightness is a generalization of convexity, and the tightness of a triangulation is a fairly restrictive property. We give a review on all known examples of tight triangulations and formulate a (computer-aided) enumeration theorem for the case of at most 15 vertices and the presence of a vertex-transitive automorphism group. Altogether, six new examples of tight triangulations are presented, a vertex-transitive triangulation of the simply connected homogeneous 5-manifold SU(3)/SO(3) with vertex-transitive action, two non-symmetric 12-vertex triangulations of S 3 × S 2, and two non-symmetric triangulations of S 3 × S 3 on 13 vertices.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1004807427002
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