A characterization of tightly triangulated 3-manifolds

Bhaskar Bagchi; Basudeb Datta; Jonathan Spreer

doi:10.1016/j.ejc.2016.10.005

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arXiv · 1601.00065

A characterization of tightly triangulated 3-manifolds

Bhaskar Bagchi·Basudeb Datta·Jonathan Spreer

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Abstract

For a field $\mathbb{F}$, the notion of $\mathbb{F}$-tightness of simplicial complexes was introduced by Kühnel. Kühnel and Lutz conjectured that any $\mathbb{F}$-tight triangulation of a closed manifold is the most economic of all possible triangulations of the manifold. The boundary of a triangle is the only $\mathbb{F}$-tight triangulation of a closed 1-manifold. A triangulation of a closed 2-manifold is $\mathbb{F}$-tight if and only if it is $\mathbb{F}$-orientable and neighbourly. In this paper we prove that a triangulation of a closed 3-manifold is $\mathbb{F}$-tight if and only if it is $\mathbb{F}$-orientable, neighbourly and stacked. In consequence, the Kühnel-Lutz conjecture is valid in dimension $\leq 3$.

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BibTeX RIS

Bhaskar Bagchi, Basudeb Datta, Jonathan Spreer. 2016-01-08. A characterization of tightly triangulated 3-manifolds. https://doi.org/10.1016/j.ejc.2016.10.005

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