The slice-ribbon conjecture for 3-stranded pretzel knots

2011/05/22 by Joshua Evan Greene, Stanislav Jabuka · 55 citations
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Advanced Combinatorial Mathematics #Ribbon #Mathematics #Conjecture #Mathematical proof #Combinatorics #Order (exchange) #Pure mathematics #Geometry

paper · doi:10.1353/ajm.2011.0022

published in American Journal of Mathematics 133(3), 555-580 (Johns Hopkins University Press)

openalex publication_date 2011/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• The orientation of Yang-Mills moduli spaces and 4-manifold topology
• Holomorphic disks and three-manifolds invariants: Properties and applications
• On the Heegaard Floer homology of branched double-covers
• Lens spaces, rational balls and the ribbon conjecture
• Holomorphic disks and topological invariants for closed three-manifolds

Cited by

• Slice implies mutant ribbon for odd 5–strandedpretzel knots
• Rational concordance of double twist knots
• Ribbon knot [wikipedia]