By use of a variety of techniques (most based on constructions of
quasipositive knots and links, some old and others new), many smooth
–manifolds
are realized as transverse intersections of complex surfaces in
with strictly
pseudoconvex
–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,
arises in infinitely many distinct ways). This survey is not comprehensive; a number
of questions are left open for future work.
Keywords
quasipositivity, contact structures on $3$–manifolds,
topological aspects of Stein theory, graph manifolds
