标题： Milnor不变量和球面链环的厚度 显示英文标题

标题： Milnor invariants and thickness of spherical links

摘要： 绳长是结或链环所需的1英寸厚绳子的最小英寸数。 这种测量值与结和链环不变量之间的关系已被多位作者研究。 我们给出了高维球面链环此类结果的首次研究，推广了第一作者与Michaelides在经典情况下的工作。 我们根据厚度找到了它们Milnor不变量的最佳渐近界，揭示了多项式和指数区域之间的二分法。 在此过程中，我们使用Massey乘积详细阐述了这些Milnor不变量及其性质。 作为应用，我们解决了Freedman和Krushkal提出的问题。 显示英文摘要

摘要： The ropelength of a knot or link is the minimal number of inches of 1-inch-thick rope that it takes to tie it. The relationship of this measurement to knot and link invariants has been studied by various authors. We give the first results of this type for higher-dimensional spherical links, generalizing work of the first author and Michaelides in the classical case. We find optimal asymptotic bounds on their Milnor invariants in terms of thickness, uncovering a dichotomy between a polynomial and an exponential regime. Along the way, we give a detailed treatment of these Milnor invariants and their properties using Massey products. As an application, we resolve a question of Freedman and Krushkal.