标题： 高阶Kirk不变量的链映射 显示英文标题

标题： Higher order Kirk invariants of link maps

摘要： 我们定义了任意数量分量的链映射的数值链同伦不变量，这些不变量自然地推广了Kirk不变量。 Kirk不变量是2分量链映射的链同伦不变量，它由每个分量的自奇异点处基于环的环绕数与另一个球面分量的环绕数给出；我们的不变量则使用Milnor的高阶链不变量的成分，并从外部的约化基本群中提取出来。 我们提供了从适当的横截面计算这些不变量的实用算法，以及由此检测到的示例族。 主要证明使用了作者之前开发的切割图的组合理论。 显示英文摘要

摘要： We define numerical link-homotopy invariants of link maps of any number of components, which naturally generalize the Kirk invariant. The Kirk invariant is a link-homotopy invariant of 2-component link maps given by linking numbers of loops based at self-singularities of each component with the other spherical component; our invariants use instead ingredients from Milnor's higher order link invariants, and are extracted from the reduced fundamental groups of the exterior. We provide practical algorithms to compute these invariants from an appropriate cross-section, as well as families of examples that are therewith detected. The main proofs use the combinatorial theory of cut-diagrams previously developed by the authors.