  If there are any 2-component counterexamples to the Generalized Property R
Conjecture, a least genus component of all such counterexamples cannot be a
fibered knot. Furthermore, the monodromy of a fibered component of any such
counterexample has unexpected restrictions.
  The simplest plausible counterexample to the Generalized Property R
Conjecture could be a 2-component link containing the square knot. We
characterize all two-component links that contain the square knot and which
surger to (S^1 x S^2) # (S^1 x S^2). We exhibit a family of such links that are
probably counterexamples to Generalized Property R. These links can be used to
generate slice knots that are not known to be ribbon.

Geometric Topology