Geometry of planar surfaces and exceptional fillings
Geometry of planar surfaces and exceptional fillings
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平面几何形状和特殊填充物
DOI：
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发表时间：
2015
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：
Neil R. Hoffman;Jessica S. Purcell
如果一个双曲三维流形允许一个例外的Dehn填充，那么这个Dehn填充的斜率长度已知至多为6。然而，六的界限似乎是尖锐的，只有在环形的情况下。在本文中，我们调查其他特殊填料的坡长。我们构造了双曲三维流形，它具有已知最长的可约填充斜率。作为一个中间步骤，我们发现，找到最长的这样的斜率的问题是等价的平面表面，这应该是独立的兴趣的最大密度horoball包装的问题。我们还讨论了其他特殊的德恩填充物的斜坡长度，并证明了6是不实现的斜坡对应的一个小塞弗特纤维空间填充。
If a hyperbolic 3‐manifold admits an exceptional Dehn filling, then the length of the slope of that Dehn filling is known to be at most six. However, the bound of six appears to be sharp only in the toroidal case. In this paper, we investigate slope lengths of other exceptional fillings. We construct hyperbolic 3‐manifolds that have the longest known slopes for reducible fillings. As an intermediate step, we show that the problem of finding the longest such slope is equivalent to a problem on the maximal density horoball packings of planar surfaces, which should be of independent interest. We also discuss lengths of slopes of other exceptional Dehn fillings, and prove that six is not realized by a slope corresponding to a small Seifert fibered space filling.
纤维三流管的尖点几何形状
影响因子：
1.7
作者：
Futer D
通讯作者：
Futer D