Suppose a genus two handlebody is removed from a 3–manifold M and
then a single meridian of the handlebody is restored. The result is a
knot or link complement in M and it is natural to ask whether
geometric properties of the link complement say something about the
meridian that was restored. Here we consider what the relation must
be between two not necessarily disjoint meridians so that restoring
each of them gives a trivial knot or a split link.
Dedicated to the memory of Heiner
Zieschang, first to notice that genus two handlebodies could
be interesting
