A characterization of tightly triangulated 3-manifolds
A characterization of tightly triangulated 3-manifolds
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紧密三角化 3 流形的表征
DOI：
10.1016/j.ejc.2016.10.005
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Spreer
中科院分区：
文献类型：
--
作者：
B. Bagchi;B. Datta;J. Spreer
对于域 F，单纯复形的 F 紧性概念是由 Kühnel 引入的。 Kühnel 和 Lutz 推测闭合流形的 F 紧三角剖分是所有可能的流形三角剖分中最经济的。三角形的边界是闭 1-流形的唯一 F 紧三角剖分。闭合 2 流形的三角剖分是 F 紧的当且仅当它是 F 方向可邻的。在本文中，我们证明了闭合 3 流形的三角剖分是 F 紧的当且仅当它是 F 可定向的、邻接的且堆叠的。因此，Kühnel-Lutz 猜想在维度≤ 3 时有效。
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.