Cusp shapes under cone deformation
Cusp shapes under cone deformation
复制标题
锥体变形下的尖点形状
DOI：
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发表时间：
2004
期刊：
影响因子：
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通讯作者：
Jessica S. Purcell
中科院分区：
文献类型：
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作者：
Jessica S. Purcell
关于双曲流形尖点的星球环面继承了欧几里得相似结构，称为尖点形状。当流形的双曲结构通过保留尖点的锥体变形而变形时，我们限制了尖点形状的变化。界限是根据单一轨迹的邻域中的结构变化来表示的。然后，我们应用该结果来提供有关许多双曲结的尖点形状的信息，仅给出结的图表。具体来说，我们证明存在一个通用常数 C，这样如果一个结允许一个质数、每个扭转区域至少有 C 个交叉的扭转简化图，则尖点环面上第二短曲线的长度是有界的。该界限与图表的扭曲区域的数量呈线性关系。
A horospherical torus about a cusp of a hyperbolic manifold inherits a Euclidean similarity structure, called a cusp shape. We bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp. The bounds are in terms of the change in structure in a neighborhood of the singular locus alone. We then apply this result to provide information on the cusp shape of many hyperbolic knots, given only a diagram of the knot. Specifically, we show there is a universal constant C such that if a knot admits a prime, twist reduced diagram with at least C crossings per twist region, then the length of the second shortest curve on the cusp torus is bounded. The bound is linear in the number of twist regions of the diagram.
影响因子：
0.7
作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584
通讯作者：
.Ilker S. Yuce-Ilker-S.-Yuce-102800584