Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures
By Robert E. Gompf, M. Scharlemann, A. Thompson. 2010
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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 1 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.
Subfields: Geometry and Topology, Neurology
View Paper: https://www.semanticscholar.org/paper/7fee4faa4e90256c140e9f9788a6daee587e9c17
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In Geometry and Topology
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