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Periodica Mathematica Hungarica

, Volume 39, Issue 1–3, pp 161–183 | Cite as

A CENSUS OF TIGHT TRIANGULATIONS

  • Wolfgang Kühnel
  • Frank H. Lutz
Article

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.

Keywords

Euclidean Space Automorphism Group Restrictive Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Wolfgang Kühnel
  • Frank H. Lutz

There are no affiliations available

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