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

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

2011-03-08

arxiv.org/abs/1103.1601v1

Geometry & Topology 14 (2010) 2305-2347

Mathematics

Geometric Topology

Combines and expands arXiv:0908.2795 and arXiv:0901.2319 into the version published in Geometry and Topology

Scientific paper

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.

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