Mathematical Research Letters

Volume 23 (2016)

Number 2

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

Pages: 303 – 323

DOI: http://dx.doi.org/10.4310/MRL.2016.v23.n2.a1

Authors

Tetsuya Abe (Advanced Mathematical Institute, Osaka City University, Sugimoto, Sumiyoshi-ku, Osaka, Japan)

Keiji Tagami (Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba, Japan)

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 counter-example to the slice-ribbon conjecture.

Keywords

Akbulut–Kirby’s conjecture, annulus twist, slice-ribbon conjecture, tight contact structure

2010 Mathematics Subject Classification

57M25, 57R65

Full Text (PDF format)