Seifert fibered manifolds and Dehn surgery, III
Seifert fibered manifolds and Dehn surgery, III
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Seifert 纤维歧管和 Dehn 手术，III
DOI：
10.4310/cag.1999.v7.n3.a3
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发表时间：
1999
影响因子：
0.7
通讯作者：
Kimihiko Motegi
中科院分区：
文献类型：
--
作者：
Katura Miyazaki;Kimihiko Motegi
如果Dehn手术产生塞弗特纤维歧管，则其被称为塞弗特纤维化手术。已经证明，非平凡的，塞弗特手术suprisons在3球的结是积分手术，除非结是平凡的结，一个环面结，或一个电缆的环面结。我们首先证明了一个类似的结果结在一个固体环面。作为一个推论，它表明，该猜想持有，如果一个经常或例外的纤维所产生的塞弗特纤维流形是unknotted（原）3-球，这一假设是验证了许多塞弗特planering手术。作为另一个应用，我们表明，除了平凡的例子，没有周期大于2的周期结产生一个塞弗特纤维流形与一个无限的基本组手术。
A Dehn surgery is called a Seifert fibering surgery if it yields a Seifert fibered manifold. It has been conjectured that nontrivial, Seifert fibering sugeries on knots in the 3-sphere are integral surgeries unless the knot is a trivial knot, a torus knot, or a cable of a torus knot. We first prove an analogous result for knots in a solid torus. As a corollary it is shown that the conjecture holds if a regular or exceptional fiber of the resulting Seifert fibered manifold is unknotted in the (original) 3-sphere; this assumption is verified for many Seifert fibering surgeries. As another application, we show that except for trivial examples, no periodic knots with period greater than 2 produce a Seifert fibered manifold with an infinite fundamental group by surgery.