Abstract
If there are any –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 –component link containing the square knot. We characterize all two-component links that contain the square knot and which surger to . 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.
Citation
Robert E Gompf. Martin Scharlemann. Abigail Thompson. "Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures." Geom. Topol. 14 (4) 2305 - 2347, 2010. https://doi.org/10.2140/gt.2010.14.2305
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