The slice-ribbon conjecture for 3-stranded pretzel knots

Abstract

We determine the smooth concordance order of the 3-stranded pretzel knots P(p,q,r) with p,q,r odd. We show that each one of finite order is, in fact, ribbon, thereby proving the slice-ribbon conjecture for this family of knots. As corollaries we give new proofs of results first obtained by Fintushel-Stern and Casson-Gordon.

21 pages, 5 figures. Significantly expanded version, mistake in previous proof corrected

Cited by in corpus (4)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• Obstructing Sliceness in a Family of Montesinos Knots
• Concordance invariants from higher order covers
• Rational Witt classes of pretzel knots