ENGLISH

A Census of Tight Triangulations

By Kuhnel W. , Lutz F. H.

Book information

Year
2000
Language
english
Format
PDF
Filesize
1 MB (1293686 bytes)
Pages
23\23
Library
mexmat
Time added
2009-11-09 02:42:13

Description

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 , and two non-symmetric triangulations of on 13 vertices.

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