半简支隧道
Semisimple tunnels
摘要：
在亏格为1的1-桥位置（称为（1，1）-位置）的3-球面中的纽结可以用环面中两点的辫群的元素来描述。我们的主要结果告诉如何转换之间的辫群元素和（1，1）-位置的上，下隧道的斜率不变量的序列。在使用它们来验证以前的计算的所有隧道的2桥结和（1，1）-隧道的环面结的斜率不变量，我们得到的2桥结隧道的斜率序列的特征，一类隧道，我们称之为环形。的主要结果导致一个通用的算法来计算的上，下隧道的编织描述的斜率不变量。该算法已实现为软件，我们给出了一些示例计算。
英文摘要：
A knot in the 3-sphere in genus-1 1-bridge position (called a (1,1)-position) can be described by an element of the braid group of two points in the torus. Our main results tell how to translate between a braid group element and the sequence of slope invariants of the upper and lower tunnels of the (1,1)-position. After using them to verify previous calculations of the slope invariants for all tunnels of 2-bridge knots and (1,1)-tunnels of torus knots, we obtain characterizations of the slope sequences of tunnels of 2-bridge knots, and of a class of tunnels we call toroidal. The main results lead to a general algorithm to calculate the slope invariants of the upper and lower tunnels from a braid description. The algorithm has been implemented as software, and we give some sample computations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
