Celebratio Mathematica — Thompson — Complete Bibliography

Complete Bibliography

Works connected to Robert E. Gompf

Filter the Bibliography List

year	title	people

			clear

R. E. Gompf, M. Scharlemann, and A. Thompson: “Fibered knots and potential counterexamples to the property \( 2{R} \) and slice-ribbon conjectures,” Geom. Topol. 14 : 4 (2010), pp. 2305–2347. MR 2740649 Zbl 1214.57008 ArXiv 1103.1601 article

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 \( \#_2(S^1\times S^2) \). 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.

Robert E. Gompf	Related
Martin Scharlemann	Related	Volume