2002/03/04 by Lee Rudolph
Mathematics · #math.GT #msc:57M25
published as Commentarii Mathematici Helvetici 62 (1987) 630-645 · HyperTeX version (correcting minor typographical errors; with addenda) prepared February 2002
arxiv created 2002/03/04 · arxiv updated 2009/11/30
From a fibered link in the 3-sphere may be constructed a field of not everywhere tangent 2-planes; when the fibered link is the link of an isolated critical point of a map from 4-space to the plane, the plane field is essentially the field of kernels of the derivative of the map. Homotopically, such a plane field determines two integers. I show that the sum of these integers is the Milnor number of the fibered link. Taking the mirror image of a link exchanges the integers. Various examples are computed. It is noted (proof given elsewhere) that these integers are not determined by the algebraic monodromy (or Seifert form) of the fibered link.