Mathematical Research Letters
Volume 23 (2016)
Fibered knots with the same $0$-surgery and the slice-ribbon conjecture
Pages: 303 – 323
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 counter-example to the slice-ribbon conjecture.
Akbulut–Kirby’s conjecture, annulus twist, slice-ribbon conjecture, tight contact structure
2010 Mathematics Subject Classification