Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures
Abstract
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.
Keywords
Cite
@article{arxiv.1103.1601,
title = {Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures},
author = {Robert E. Gompf and Martin Scharlemann and Abigail Thompson},
journal= {arXiv preprint arXiv:1103.1601},
year = {2011}
}
Comments
Combines and expands arXiv:0908.2795 and arXiv:0901.2319 into the version published in Geometry and Topology