Non-integral Toroidal Dehn Surgeries
Non-integral Toroidal Dehn Surgeries
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非整体环形 Dehn 手术
DOI：
10.4310/cag.2004.v12.n1.a18
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发表时间：
2004
影响因子：
0.7
通讯作者：
C. Gordon
中科院分区：
文献类型：
--
作者：
J. Luecke;C. Gordon
如果我们对三维球面中的双曲纽结进行非平凡的Dehn手术，结果通常是一个双曲三维流形。但也有例外：有双曲结的手术，使透镜空间[1]，小塞弗特纤维空间[2]，[5]，[7]，[19]，和环面流形，即包含（嵌入）不可压缩环面的流形[6]，[7]。特别地，Eudave-Muñoz [6]明确地描述了双曲结k（，m，n，p）的无限族，每个双曲结具有特定的半积分环面手术。（这些是唯一已知的非平凡、非积分、非双曲的双曲结手术的例子。在这里，我们表明，这些结是唯一的双曲结与非积分环形手术。
If we perform a non-trivial Dehn surgery on a hyperbolic knot in the 3sphere, the result is usually a hyperbolic 3-manifold. However, there are exceptions: there are hyperbolic knots with surgeries that give lens spaces [1], small Seifert fiber spaces [2], [5], [7], [19], and toroidal manifolds, that is, manifolds containing (embedded) incompressible tori [6], [7]. In particular, Eudave-Muñoz [6] has explicitly described an infinite family of hyperbolic knots k( ,m, n, p), each of which has a specific half-integral toroidal surgery. (These are the only known examples of non-trivial, non-integral, non-hyperbolic surgeries on hyperbolic knots.) Here we show that these knots are the only hyperbolic knots with non-integral toroidal surgeries.