Lens spaces, rational balls and the ribbon conjecture

2007/01/22 by Paolo Lisca · 124 citations
Mathematics · #Advanced Operator Algebra Research #Bridge (graph theory) #Combinatorics #Conjecture #Geometric and Algebraic Topology #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Intersection (aeronautics) #Knot (papermaking) #Lens space #Mathematics #Pure mathematics #Ribbon #math.GT #msc:57M25

paper · pdf · doi:10.2140/gt.2007.11.429

published in Geometry & Topology 11(1), 429-472 (Mathematical Sciences Publishers) · 45 pages, 8 figures; accepted for publication in Geometry and Topology

arxiv created 2007/01/22 · openalex publication_date 2007/03/16 · arxiv updated 2014/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We apply Donaldson's theorem on the intersection forms of definite 4-manifolds to characterize the lens spaces which smoothly bound rational homology 4-dimensional balls. Our result implies, in particular, that every smoothly slice 2-bridge knot is ribbon, proving the ribbon conjecture for 2-bridge knots. 57M25

Citations

• The orientation of Yang-Mills moduli spaces and 4-manifold topology
• Deformationen von Quotientensingularit�ten (nach zyklischen Gruppen)

Cited by

• Knot concordance and Heegaard Floer homology invariants in branched covers
• Branched covers bounding rational homology balls
• The slice-ribbon conjecture for 3-stranded pretzel knots
• Slice implies mutant ribbon for odd 5–strandedpretzel knots
• Rational concordance of double twist knots
• Ribbon knot [wikipedia]