标题： 沿纽结的唯一手术描述 显示英文标题

标题： Unique Surgery Descriptions along Knots

摘要： 我们证明对于任何非平凡的扭结K，沿K的无限多个r-手术K(r)在扭结上有唯一的手术描述。 此外，我们表明对于任何双曲L-空间扭结K和无限多个整数斜率n，流形K(n)有唯一的手术描述。 在这里，我们说一个3-流形M在S^3中的扭结上有唯一的手术描述，如果存在唯一的扭结K和斜率r的对，使得M与K(r)在保持方向的微分同胚下相同。 这推广了特征斜率的概念。 相反，我们提供了新的具有多个不同手术描述的流形家族。 更准确地说，我们为每个非零整数m构造了一个扭结K_m，使得对于任何整数n，流形K_m(m+1/n)也可以通过另一个扭结的手术得到。 显示英文摘要

摘要： We prove that for any non-trivial knot K, infinitely many r-surgeries K(r) along K have a unique surgery description along a knot. Moreover, we show that for any hyperbolic L-space knot K and infinitely many integer slopes n, the manifold K(n) has a unique surgery description. Here we say a 3-manifold M has a unique surgery description along a knot in S^3 if there is a unique pair (K,r) of a knot K and a slope r such that M is orientation-preservingly diffeomorphic to K(r). This generalises the notion of characterising slopes. Conversely, we provide new families of manifolds with several distinct surgery descriptions along knots. More precisely, we construct for every non-zero integer m a knot K_m such that for any integer n, the manifold K_m(m+1/n) can also be obtained by surgery on another knot.