A characterization of tightly triangulated 3-manifolds

Article Type

Research Article

Publication Title

European Journal of Combinatorics

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.

First Page

133

Last Page

137

DOI

10.1016/j.ejc.2016.10.005

Publication Date

3-1-2017

Comments

Open Access, Green

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