Infinitely Many Knots Admitting the Same Integer Surgery and a Four-Dimensional Extension
Infinitely Many Knots Admitting the Same Integer Surgery and a Four-Dimensional Extension
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无限多个结允许相同的整数手术和四维扩展
DOI：
10.1093/imrn/rnv008
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发表时间：
2015
影响因子：
1
通讯作者：
John Luecke and John Osoinach
中科院分区：
文献类型：
--
作者：
Tetsuya Abe;In Dae Jong;John Luecke and John Osoinach
我们证明了对于任意整数，存在无穷多个不同的纽结，使得对这些纽结的-外科手术产生相同的-流形。特别是，当同源球从这些手术中产生。这回答了Kirby问题列表上的问题3.6（D）。我们构建两个家庭的例子，第一个通过扭曲的方法沿着一个环和第二个通过推广这个过程。后一个族也解决了问题3.6（D）的一个更强的版本，即对于任何整数，存在无穷多个相互不同的纽结，使得每个带框架的2-柄加法沿着产生相同的流形。
We prove that for any integerthere exist infinitely many different knots insuch that-surgery on those knots yields the same-manifold. In particular, whenhomology spheres arise from these surgeries. This answers Problem 3.6(D) on the Kirby problem list. We construct two families of examples, the first by a method of twisting along an annulus and the second by a generalization of this procedure. The latter family also solves a stronger version of Problem 3.6(D), that for any integer, there exist infinitely many mutually distinct knots such that 2-handle addition along each with framingyields the same-manifold.