论文标题
通过Dehn Filling获得的3个体的复杂性
Complexity of 3-manifolds obtained by Dehn filling
论文作者
论文摘要
令$ m $为紧凑型3 - 具有边界的manifold。我们提出了封闭3的上下复杂性界限，即使是$ M的dehn填充物获得的manifolds作为应用程序，我们表征了一些无限的dehn填充物的$ m $的家族，我们的方法将其成员的复杂性确定为添加剂常数。常数仅取决于$ m $选择的三角剖分的大小以及其边界的同位素类别。 然后，我们表明，鉴于三角元的$ \ mathcal t $ $ m $，$ 2 $ - 三角形的圆环边界，存在什至是$ m $的无限家庭，我们可以确定填充流形的复杂性，并在最多$ 13 | \ nathcal t | \ nathcal t | flap | + 7. $此结果被引导以获得差距，这是$ m $的理想三角剖分的大小或结图的交叉数。我们还展示了如何计算三个球体中填充填充物的明确填充物的差距。通过确定数字八节的偶数填充物，椒盐脆饼结$ p（-2,3,7）$和Trefoil的几个无限家族的复杂性，可以证明我们方法的实用性。
Let $M$ be a compact 3--manifold with boundary a single torus. We present upper and lower complexity bounds for closed 3--manifolds obtained as even Dehn fillings of $M.$ As an application, we characterise some infinite families of even Dehn fillings of $M$ for which our method determines the complexity of its members up to an additive constant. The constant only depends on the size of a chosen triangulation of $M$, and the isotopy class of its boundary. We then show that, given a triangulation $\mathcal T$ of $M$ with $2$--triangle torus boundary, there exist infinite families of even Dehn fillings of $M$ for which we can determine the complexity of the filled manifolds with a gap between upper and lower bound of at most $13 |\mathcal T| + 7.$ This result is bootstrapped to obtain the gap as a function of the size of an ideal triangulation of the interior of $M$, or the number of crossings of a knot diagram. We also show how to compute the gap for explicit families of fillings of knot complements in the three-sphere. The practicability of our approach is demonstrated by determining the complexity up to a gap of at most 10 for several infinite families of even fillings of the figure eight knot, the pretzel knot $P(-2,3,7)$, and the trefoil.
