Fibered knots with the same $0$-surgery and the slice-ribbon conjecture

Abstract

Akbulut and Kirby conjectured that two knots with the same $0$-surgery are concordant. In this paper, we prove that if the slice-ribbon conjecture is true, then the modified Akbulut-Kirby's conjecture is false. We also give a fibered potential counterexample to the slice-ribbon conjecture.

15 pages, 9 figures; Final version. In version 4, Abstract is mistakenly deleted

References in corpus (2)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (2)

• Corks, exotic 4-manifolds and knot concordance
• A survey of the homology cobordism group