On hyperbolic knots with Seifert fibered Dehn surgeries
On hyperbolic knots with Seifert fibered Dehn surgeries
复制标题
用 Seifert 纤维 Dehn 手术治疗双曲线结
DOI：
10.1016/s0166-8641(01)00114-6
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发表时间：
2002
影响因子：
0.6
通讯作者：
M. Eudave
中科院分区：
文献类型：
--
作者：
M. Eudave
J.C. Dean描述了一种结构，它产生了一个小的Seifert纤维歧管Dehn手术结。我们将这种构造转化为缠结，并证明当且仅当相应的覆盖结满足Dean条件时，可琐屑缠结满足一定的条件。这可以用来证明所有已知的双曲结产生塞弗特纤维流形的例子，这些例子是由蒙特西诺斯的技巧构造的，实际上可以通过Dean的构造得到。我们稍微扩展了Dean的构造，为了包括手术产生带有轨道表面的Seifert纤维流形一个投影平面和两个特殊的纤维，我们展示了无限族的双曲结有这种手术。
J.C. Dean has described a construction which produces knots having a small Seifert fibered manifold Dehn surgery. We translate this construction to tangles, and show that a trivializable tangle satisfies certain conditions if and only if the corresponding covering knot satisfies Dean's conditions. This can be used to show that all known examples of hyperbolic knots producing Seifert fibered manifolds, which were constructed by Montesinos's trick, can in fact be obtained by Dean's construction. We extend Dean's construction slightly, in order to include surgeries producing Seifert fibered manifolds with orbit surface a projective plane and two exceptional fibers, and we show an infinite family of hyperbolic knots having that kind of surgery.