Volume 14, issue 4 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2487–3110
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Fibered knots and potential counterexamples to the Property 2R and Slice-Ribbon Conjectures

Robert E Gompf, Martin Scharlemann and Abigail Thompson

Geometry & Topology 14 (2010) 2305–2347
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 #2(S1 × S2). 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
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
Authors
Robert E Gompf
Mathematics Department
University of Texas at Austin
1 University Station C1200
Austin TX 78712-0257
USA
Martin Scharlemann
Mathematics Department
University of California, Santa Barbara
Santa Barbara CA 93106
USA
http://www.math.ucsb.edu/~mgscharl/
Abigail Thompson
Mathematics Department
University of California, Davis
Davis CA 95616
USA
http://www.math.ucdavis.edu/~thompson/