A construction of slice knots via annulus twists

Abstract

We give a new construction of slice knots via annulus twists. The simplest slice knots obtained by our method are those constructed by Omae. In this paper, we introduce a sufficient condition for given slice knots to be ribbon, and prove that all Omae's knots are ribbon.

26 pages and 28 figures. Comments are welcome.Version 2: A new section added. Version 3: The definition of an annulus twist was clarified. The anonymous referee pointed out a gap of Theorem 3.1. The statement of Theorem 3.1 was weakened. Version 4: Abstract, Introduction and Section 6 are rewritten

References in corpus (4)

• Corks, Plugs and exotic structures
• Bridge number and integral Dehn surgery
• Nash homotopy spheres are standard
• Counterexamples to Kauffman's Conjectures on Slice Knots

Cited by in corpus (3)

• Annulus twist and diffeomorphic 4-manifolds II
• Infinitely many knots admitting the same integer surgery and a 4-dimensional extension
• Shadows and quantum invariants