论文标题
3型脉络
Transfinite Milnor invariants for 3-manifolds
论文作者
论文摘要
约翰·米尔诺（John Milnor）在1957年的论文中介绍了链接不变式，该链接不变型相对于链接小组的下中央系列的链路的纵向类别。因此，这些不变性确定了链接组的较低中央系列商。这项工作使数十年的研究具有深远的影响。米尔诺（Milnor）的原始问题之一尚未解决：从链接组的跨大小下中央系列中提取类似的不变性。我们将Milnor的不变性在更广泛的3个Manifolds的环境中重新制定，并以他的原始不变性为特殊情况。我们为米尔诺（Milnor）对一般三曼群群体的问题提出了解决方案，开发了跨足的不变性理论并实现了非平凡的价值。
In his 1957 paper, John Milnor introduced link invariants which measure the homotopy class of the longitudes of a link relative to the lower central series of the link group. Consequently, these invariants determine the lower central series quotients of the link group. This work has driven decades of research with profound influence. One of Milnor's original problems remained unsolved: to extract similar invariants from the transfinite lower central series of the link group. We reformulate and extend Milnor's invariants in the broader setting of 3-manifolds, with his original invariants as special cases. We present a solution to Milnor's problem for general 3-manifold groups, developing a theory of transfinite invariants and realizing nontrivial values.
