Dehn Filling of the "Magic" 3-manifold
Dehn Filling of the "Magic" 3-manifold
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DOI：
10.4310/cag.2006.v14.n5.a6
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发表时间：
2002-04
影响因子：
0.7
通讯作者：
B. Martelli;C. Petronio
中科院分区：
文献类型：
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作者：
B. Martelli;C. Petronio
我们对具有 3 个分量的链环补集的所有非双曲 Dehn 填充进行分类，推测为具有 3 个尖点的最小双曲 3 流形。我们推导出无限多个 1 尖点和 2 尖点双曲流形的所有非双曲 Dehn 填充的分类，包括大多数已知体积最小的流形。在这种分类的其他后果中，我们提到以下内容： - 对于每个整数 n，我们可以证明 3-球体中有无限多个双曲结，具有特殊的手术 n、n+1、n+2、n+3，其中 n+1、n+2 给出小 Seifert 流形，n、n+3 给出环形流形； - 我们展示了一个 2 尖点双曲流形，其中包含一对具有同胚补的不等价结； -我们展示了一个手性3流形，其中包含一对不等价的双曲结，具有保持方向的同胚补体； - 我们为小型 Seifert 填充物和任何其他类型的特殊填充物之间的最大距离给出了明确的下限。
We classify all the non-hyperbolic Dehn fillings of the complement of the chain-link with 3 components, conjectured to be the smallest hyperbolic 3-manifold with 3 cusps. We deduce the classification of all non-hyperbolic Dehn fillings of infinitely many 1-cusped and 2-cusped hyperbolic manifolds, including most of those with smallest known volume. Among other consequences of this classification, we mention the following: - for every integer n we can prove that there are infinitely many hyperbolic knots in the 3-sphere having exceptional surgeries n, n+1, n+2, n+3, with n+1, n+2 giving small Seifert manifolds and n, n+3 giving toroidal manifolds; - we exhibit a 2-cusped hyperbolic manifold that contains a pair of inequivalent knots having homeomorphic complements; - we exhibit a chiral 3-manifold containing a pair of inequivalent hyperbolic knots with orientation-preservingly homeomorphic complements; - we give explicit lower bounds for the maximal distance between small Seifert fillings and any other kind of exceptional filling.