[Topology and Geometry Seminar] Unlinking singular locus from regular fibers and its application to submersions by Dr. Osamu Saeki

Given a link L in a closed oriented 3-manifold, we determine those links
in its complement which can be realized as the singular point set of
a generic smooth map of the 3-manifold into the plane having the link L
as a regular fiber. Then, we study the linking behavior between
the singular point set and regular fibers for generic smooth maps of
3-manifolds into the plane. As an application, we give
new techniques for constructing submersions of open 3-manifolds
into the plane having a given link as a regular fiber.