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

References in corpus (2)

• Knot Floer homology and the four-ball genus
• On the Floer homology of plumbed three-manifolds

Cited by in corpus (6)

• Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
• On closed 3-braids with unknotting number one
• Obstructing Sliceness in a Family of Montesinos Knots
• Concordance invariants from higher order covers
• Rational Witt classes of pretzel knots
• On the Slice-Ribbon Conjecture for Montesinos knots