Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures

@inproceedings{Gompf2010FiberedKA,
  title={Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures},
  author={Robert E. Gompf and Martin Scharlemann and Abigail E Thompson},
  year={2010}
}
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 twocomponent links that contain the square knot and which surger to #2.S… CONTINUE READING

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