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Efficient triangulations and boundary slopes

机译:高效的三角和边界斜坡

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For a compact, orientable, irreducible, partial differential -irreducible, and an-annular 3-manifold, it is shown there are only finitely many boundary slopes for incompressible and partial differential -incompressible surfaces of a bounded Euler characteristic. We use normal surface theory and the inverse relationship of crushing a triangulation along a normal surface [8] and that of inflating an ideal triangulation [12] to introduce and study boundary-efficient triangulations and end-efficient ideal triangulations. It is shown for a compact 3-manifold with boundary, satisfying these topological conditions, any triangulation can be modified to a boundary-efficient triangulation; furthermore, it can be decided if a triangulation of such a manifold is boundary-efficient. (c) 2021 Elsevier B.V. All rights reserved.
机译:对于紧凑,可定向,不可可动化,部分差分 - 倍差和环形3 - 歧管,示出了仅存在有界欧拉特征的不可压缩和部分差异的尺寸抑制表面的许多边界斜率。 我们使用正常表面理论和沿正常表面[8]粉碎三角测量的逆关系,并膨胀理想的三角测量[12]以引入和研究边界有效的三角形和最终有效的理想三角形。 它显示为具有边界的紧凑3歧管,满足这些拓扑条件,任何三角测量都可以被修改为边界有效的三角测量; 此外,如果这种歧管的三角测量是基于效率的,则可以确定。 (c)2021 Elsevier B.V.保留所有权利。

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