We extend techniques due to Pardon to show that there is a lower bound on the distortion of a knot in ${\mathbb{R}}^3$ proportional to the minimum of the bridge distance and the bridge number of the knot. We also exhibit an infinite family of knots for which the minimum of the bridge distance and the bridge number is unbounded and Pardon's lower bound is constant.

中文翻译：

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扭曲和结的桥距

我们扩展了由于Pardon而产生的技术，以表明在 ${\mathbb{[R}}^3$与桥距和结的桥数的最小值成正比。我们还展示了一个无限的结系列，其最小的桥距和桥数不受限制，Pardon的下限恒定。