Dehn filling and the geometry of unknotting tunnels
Dehn filling and the geometry of unknotting tunnels
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Dehn 填充和解结隧道的几何形状
DOI：
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发表时间：
2011
期刊：
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通讯作者：
Jessica S. Purcell
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文献类型：
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作者：
D. Cooper;D. Futer;Jessica S. Purcell
通过Dehn对双尖点双曲流形的尖点进行填充，得到了任意单尖点双曲流形M的非打结隧道。在M是由“一般”Dehn填充得到的情况下，我们证明了它是一条测地线的同位素，并刻画了它在M的正则分解中是否是一条边的同位素。我们也给出了明确的估计（仅加性误差）的长度相对于一个最大的尖点。这些结果对亚当斯、佐久间和威克斯提出的三个长期存在的问题给出了一般性的答案。我们还构造了一个显式序列的单隧道结在S3，所有的unknotting隧道的长度接近无穷大。57M25、57M50、57R52
Any one-cusped hyperbolic manifold M with an unknotting tunnel is obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the case where M is obtained by “generic” Dehn filling, we prove that is isotopic to a geodesic, and characterize whether is isotopic to an edge in the canonical decomposition of M . We also give explicit estimates (with additive error only) on the length of relative to a maximal cusp. These results give generic answers to three long-standing questions posed by Adams, Sakuma and Weeks. We also construct an explicit sequence of one-tunnel knots in S 3 , all of whose unknotting tunnels have length approaching infinity. 57M25, 57M50, 57R52