AI 中文总结
研究三维球面中两个不同纽结共享德恩手术数量问题，基于纽结外部的JSJ分解给出证明，为共享手术最大数量提供有效界。
AI 中文摘要
一个民间定理表明，对于三维球面\(S^3\)中任意一对不同的纽结，对每个纽结进行\(p/q\)-德恩手术，至多有有限多个斜率\(p/q\)能得到保向同胚的流形。本文基于纽结外部的JSJ分解给出证明，为任意给定的不同纽结对之间共享手术的最大数量提供了有效界。
英文摘要
A folklore theorem states that for any pair of distinct knots in $S^3$, performing $p/q$-Dehn surgery on each knot yields orientation-preservingly homeomorphic manifolds for at most finitely many slopes $p/q$. In this paper, we provide a proof based on the JSJ decomposition of knot exteriors. In particular, for any given pair of distinct knots, it provides an effective bound on the maximal number of shared surgeries between the knots.
CommentsComments welcome. 11 pages, 2 tables
