J. H. C. Whitehead给出了从3-球面到2-球面的光滑映射p的Hopf不变量H（p）的一个优美的积分公式。给定一个在3-球面上的开卷结构b（或者，本质上等价地，一个从4-空间到平面的映射F的孤立临界点），怀特海公式可以“沿着纤维积分”，将H（p）表示为某个1-形式在圆上的积分。在p与b（或F）几何相关的情况下-例如，如果p是映射（F的纤维广义高斯映射的一个分量），其Hopf不变量lambda（K）是与F（或b）相关联的3-球面中纤维链K的“Milnor数的增强”，作者和其他人以前研究过-可能希望这种1-形式具有几何意义。本说明以几个猜测和问题的形式使这一希望更加具体。
英文摘要：
J. H. C. Whitehead gave an elegant integral formula for the Hopf invariant H(p) of a smooth map p from the 3-sphere to the 2-sphere. Given an open book structure b on the 3-sphere (or, essentially equivalently, an isolated critical point of a map F from 4-space to the plane), Whitehead's formula can be "integrated along the fibers" to express H(p) as the integral of a certain 1-form over the circle. In case p is geometrically related to b (or F) -- for instance, if p is the map (one component of the fiberwise generalized Gauss map of F) whose Hopf invariant lambda(K) is the "enhancement of the Milnor number" of the fibered link K in the 3-sphere associated to F (or b), previously studied by the author and others -- it might be hoped that this 1-form has geometric significance. This note makes that hope somewhat more concrete, in the form of several speculations and questions.
Isolated critical points of mappings from $\mathbf{R}^4$ to $\mathbf{R}^2$ and a natural splitting of the Milnor number of a classical fibered link. Part I: Basic theory; examples
Invariance of Milnor numbers and topology of complex polynomials
本文给出了多项式的Le-Ramanujam μ常数定理的一个整体形式。设f_t（t in [0，1]）是一族具有孤立奇点的n个复变数，其系数是t中的多项式。我们考虑的情况下，一些数值不变量是常数（仿射Milnor数，Milnor数在无穷远，临界值的数量，仿射临界值的数量，临界值在无穷远）。设n=2，f_t的次数为常数，则多项式f_0与f_1拓扑等价。当n>3时，假设无穷远处的临界值连续依赖于t，则证明了f_t的几何单值表示都是等价的。
