论文标题
链接数及其渐近行为的基于不变的公式的证明
A Proof of the Invariant Based Formula for the Linking Number and its Asymptotic Behaviour
论文作者
论文摘要
1833年，高斯在3空间中定义了两条不相交曲线的链接数。对于开放曲线，这种在参数化曲线上的双重积分是实现的，并且不变的模量刚性运动或等轴形成可保留点之间距离的距离，并且最近已用于阐明分子结构。 1976年，Banchoff几何解释了两个线段之间的链接数。基于此解释的明确分析公式在2000年给出，没有6个等轴测不变的证据：段和4个坐标之间的距离和角度指定其相对位置。我们给出了此公式的详细证明，并描述了以前未研究的渐近行为。
In 1833 Gauss defined the linking number of two disjoint curves in 3-space. For open curves this double integral over the parameterised curves is real-valued and invariant modulo rigid motions or isometries that preserve distances between points, and has been recently used in the elucidation of molecular structures. In 1976 Banchoff geometrically interpreted the linking number between two line segments. An explicit analytic formula based on this interpretation was given in 2000 without proof in terms of 6 isometry invariants: the distance and angle between the segments and 4 coordinates specifying their relative positions. We give a detailed proof of this formula and describe its asymptotic behaviour that wasn't previously studied.
