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Fibered knots and
potential counterexamples to the Property 2R and Slice-Ribbon
Conjectures
Robert E Gompf, Martin Scharlemann and Abigail Thompson |
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Geometry & Topology 14 (2010) 2305–2347
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Abstract |
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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. |
Keywords
Property R, Slice-Ribbon Conjecture, Andrews–Curtis moves
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References |
Publication
Received: 21 January 2010
Revised: 24 August 2010
Accepted: 29 September 2010
Published: 20 November 2010
Proposed: Rob Kirby
Seconded: Mike Freedman, Colin Rourke
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Authors |
| Robert E Gompf | |
| Mathematics Department University of Texas at Austin 1 University Station C1200 Austin TX 78712-0257 USA |
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| Martin Scharlemann | |
| Mathematics Department University of California, Santa Barbara Santa Barbara CA 93106 USA |
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| http://www.math.ucsb.edu/~mgscharl/ | |
| Abigail Thompson | |
| Mathematics Department University of California, Davis Davis CA 95616 USA |
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| http://www.math.ucdavis.edu/~thompson/ | |
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