Foliations of knot complements in the bicylinder boundary

In this expository paper, we shall analyze a particularly important class of examples of surfaces and hypersurfaces in Euclidean 4-space, namely those which arise by considering real 4-space as the space of twocomplex variablesz andw and by taking geometric loci of the formf(z,w)=0 or hypersurfaces associated with such loci. Such surfaces and hypersurfaces are important in the study of the singularities of algebraic curves, as described for example in the book of Milnor 3], and they have been used recently in the construction of foliations of the 3-dimensional sphere by Lawson 2]. The examples of this paper were first presented at the International Symposium of Dynamical Systems and Foliations at Salvador in the summer of 1971, and the author expresses his gratitude for the opportunity to participate in that conference. The examples constructed in this paper are closely related to another paper of the author 1] concerning minimal surfaces in the bicylinder boundary.