Cusp shape and tunnel number
Cusp shape and tunnel number
复制标题
尖点形状和隧道数量
DOI：
10.1090/proc/14336
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发表时间：
2017
影响因子：
1
通讯作者：
Jessica S. Purcell
中科院分区：
文献类型：
--
作者：
V. Dang;Jessica S. Purcell
我们证明了双曲隧道一号流形的尖点形状集在环面的Teichmuller空间中是稠密的。因此，有无穷多个双曲隧道一号流形，最多有一个例外的Dehn填充。类似的结果也适用于隧道数为n的流形。这与大体积的Berge结相反，Berge结是隧道一号流形，但具有收敛到Teichmuller空间中的单个点的尖点形状。
We show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. As a consequence, there are infinitely many hyperbolic tunnel number one manifolds with at most one exceptional Dehn filling. A similar result holds for tunnel number n manifolds. This is in contrast to large volume Berge knots, which are tunnel number one manifolds, but with cusp shapes converging to a single point in Teichmuller space.