Some 3-dimensional transverse \(\mathbb{C}\)-links (constructions of higher-dimensional \(\mathbb{C}\)-links, I) (Q906853)

This paper was written as a survey on \(3\)-dimensional transverse \(\mathbb C\)-links, and contains several unanswered questions, proposed for future work. Using a variety of techniques such as old and new constructions of quasipositive links including quasipositive satellites, strongly quasipositive links, partially reoriented Hopf links, quasipositive fibred links, quasipositive links with distinct \(\mathbb C\)-spans, quasipositive orientations of unoriented links, the author shows how many smooth \(3\)-manifolds are realized as transverse intersections of complex surfaces in \(\mathbb C^3\) with strictly pseudoconvex \(5\)-spheres. These manifolds not only inherit interesting intrinsic structures, but also exhibit extrinsic structures of a knot-theoretical nature. For the entire collection see [Zbl 1333.57003].