Exceptional surgeries on (-2,p,p)-pretzel knots
Exceptional surgeries on (-2,p,p)-pretzel knots
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(-2,p,p)-椒盐结结的出色手术
DOI：
10.1016/j.topol.2011.11.012
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发表时间：
2012
影响因子：
0.6
通讯作者：
Y.Kabaya
中科院分区：
文献类型：
--
作者：
K.Ichihara;I.D.Jong;Y.Kabaya
我们给出了对p小于5的（−2,p,p）类型的椒盐卷饼结的特殊手术的完整描述。众所周知，这样一个结承认一个独特的环面手术产生一个独特的不可压缩环面的环面流形。通过沿环面切割，我们得到两个连通分量，其中一个是克莱因瓶上的扭曲i束。我们证明了另一个矩阵与在幻流形上用Dehn填充得到的矩阵是同胚的。另一方面，我们证明所有这些椒盐卷饼结都不允许塞弗特纤维手术。
We give a complete description of exceptional surgeries on pretzel knots of type (−2,p,p) with p⩾5. It is known that such a knot admits a unique toroidal surgery yielding a toroidal manifold with a unique incompressible torus. By cutting along the torus, we obtain two connected components, one of which is a twisted I-bundle over the Klein bottle. We show that the other is homeomorphic to the one obtained by certain Dehn filling on the magic manifold. On the other hand, we show that all such pretzel knots admit no Seifert fibered surgeries.