Consider a knot K in S3 with charge uniformly distributed on it. From the standpoint of both physics and knot theory, it is natural to try to understand the critical points of the potential and their behavior. We show the number of critical points of the potential is at least 2t(K)+2, where t(K) is the tunnel number, defined as the smallest number of arcs one must add to K such that its complement is a handlebody. The result is proven using Morse theory and stable manifold theory.

中文翻译：

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结电势临界点的下界

考虑一个结ķ在小号3电荷均匀分布在其上。从物理学和纽结理论的角度来看，尝试理解势的临界点及其行为是很自然的。我们显示势的临界点数至少为2吨(ķ)+2， 在哪里吨(ķ)是隧道编号，定义为必须添加到的最小弧数ķ这样它的补码就是一个把手。使用莫尔斯理论和稳定流形理论证明了结果。