Some 3-dimensional transverse C-links (Constructions of higher-dimensional C-links, I)

Abstract

By use of a variety of techniques (most based on constructions of quasipositive knots and links, some old and others new), many smooth 3-manifolds are realized as transverse intersections of complex surfaces in complex 3-space with strictly pseudoconvex 5-spheres. These manifolds not only inherit interesting intrinsic structures (eg, they have canonical Stein-fillable contact structures), they also have extrinsic structures of a knot-theoretical nature (eq, the 3-sphere arises in infinitely many distinct ways). This survey is not comprehensive; a number of questions are left open for future work.