  It is shown that every knot or link is the set of complex tangents of a
3-sphere smoothly embedded in the three-dimensional complex space. We show in
fact that a one-dimensional submanifold of a closed orientable 3-manifold can
be realised as the set of complex tangents of a smooth embedding of the
3-manifold into the three-dimensional complex space if and only if it
represents the trivial integral homology class in the 3-manifold. The proof
involves a new application of singularity theory of differentiable maps.
