透镜空间和滤过器的可复位手术
Reducible surgery in lens spaces and seiferters
摘要：
Cabling猜想指出，对$S^3$中的双曲结进行手术永远不会产生可约流形。与此相反，在一些非主要手术的透镜空间中确实存在双曲结。贝克构建了一个家庭这样的双曲结，并提出了一个猜想，他的例子包括所有双曲结的透镜空间与非素手术。利用塞弗特斯的思想，我们构造了这个猜想的一个反例。在构建过程中，我们还推导出了一个小塞弗特腔的阻塞，可以通过手术获得塞弗特腔。
英文摘要：
The Cabling Conjecture states that surgery on hyperbolic knots in $S^3$ never produces reducible manifolds. In contrast, there do exist hyperbolic knots in some lens spaces with non-prime surgeries. Baker constructed a family of such hyperbolic knots and posed a conjecture that his examples encompass all hyperbolic knots in lens spaces with non-prime surgeries. Using the idea of seiferters we construct a counterexample to this conjecture. In the process of construction, we also derive an obstruction for a small Seifert fibred space to be obtainable by a surgery with a seiferter.
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