Manifolds obtained by surgery on an infinite number of knots in S3
Manifolds obtained by surgery on an infinite number of knots in S3
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在 S3 中通过对无限个结进行手术获得的流形
DOI：
10.1016/j.top.2006.02.001
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
J. Osoinach
中科院分区：
文献类型：
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作者：
J. Osoinach
在S3中，利用链环上的Dehn运算构造三维流形是三维流形分类中的一项重要技术。本文描述了一种构造S3中不同双曲纽结的无限集合的方法，该集合允许进行产生相同流形的纵向运算。在一种情况下，每个构造的纽结都接受产生相同双曲流形的纵向手术；在另一种情况下，纽结接受产生相同环形流形的纵向手术。这肯定地回答了Kirby在Kirby问题列表中提出的一个问题[R.Kirby(编辑)，Problems in Low-DimensionTopology，in：GeometryTopology，American Digital Society/International Press，1997]，该问题询问是否存在同调的3-球面或任何3-流形，该3-球面或任何3-流形可以通过对无限多个不同的纽结进行n次手术而获得。
The construction of 3-manifolds via Dehn surgery on links in S3is an important technique in the classification of 3-manifolds. This paper describes a method of constructing infinite collections of distinct hyperbolic knots in S3which admit a longitudinal surgery yielding the same manifold. In one case, the knots constructed each admit a longitudinal surgery yielding the same hyperbolic manifold; in another case, the knots admit a longitudinal surgery yielding the same toroidal manifold. This answers a question formulated by Kirby in the Kirby problem list [R. Kirby (Ed.), Problems in low-dimensional topology, in: Geometric Topology, American Mathematical Society/International Press, 1997] in the affirmative, which asks if there is a homology 3-sphere, or any 3-manifold, that can be obtained by n surgery on an infinite number of distinct knots.