On Distortion and Thickness of Knots
On Distortion and Thickness of Knots
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关于结的变形和厚度
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
John M. Sullivan
中科院分区：
文献类型：
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作者：
R. Kusner;John M. Sullivan
打一个特定的结需要多长的绳子（给定直径）？或者，把问题转过来，给定一条嵌入曲线，曲线的正则邻域也嵌入了多厚？直觉上，可能的绳子的直径由结中最近交叉处的股之间的距离限定。但是，当然，当两点在曲线上相互接近时，沿着的两点之间的距离趋于零，所以为了使概念精确，我们需要排除对角线的某些邻域。
What length of rope (of given diameter) is required to tie a particular knot ? Or, to turn the problem around, given an embedded curve, how thick a regular neighborhood of the curve also is embedded ? Intuitively, the diameter of the possible rope is bounded by the distance between strands at the closest crossing in the knot. But of course the distance between two points along a curve goes to zero as the points approach each other, so to make the notion precise, we need to exclude some neighborhood of the diagonal.