关于三维流形中零同伦框架链的Kirby演算
On Kirby calculus for null-homotopic framed links in 3-manifolds
摘要：
柯比证明了S^3中的两个框架链环给出外科手术的保向同胚结果当且仅当这两个链环通过称为稳定化和双滑动的两种移动序列相关联。Fenn和Rourke给出了一个充要条件，使得在一个闭的定向三维流形中的两个框架链环通过这些移动的一个有限序列相关联。本文件有两个目的。本文首先将Fenn和Rourke的结果推广到带边界的三维流形上。然后，我们将这一结果的情况下，框架链接的组件是零同伦的3流形。
英文摘要：
Kirby proved that two framed links in S^3 give orientation-preserving homeomorphic results of surgery if and only if these two links are related by a sequence of two kinds of moves called stabilizations and handle-slides. Fenn and Rourke gave a necessary and sufficient condition for two framed links in a closed, oriented 3-manifold to be related by a finite sequence of these moves. The purpose of this paper is twofold. We first give a generalization of Fenn and Rourke's result to 3-manifolds with boundary. Then we apply this result to the case of framed links whose components are null-homotopic in the 3-manifold.
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