Lens spaces, rational balls and the ribbon conjecture

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.

45 pages, 8 figures; accepted for publication in Geometry and Topology

Cited by in corpus (41)

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• On the slice-ribbon conjecture for pretzel knots
• Dehn surgeries and rational homology balls
• Stein fillable Seifert fibered 3-manifolds
• The topological sliceness of 3-strand pretzel knots
• Equivalence of symmetric union diagrams
• Average four-genus of two-bridge knots
• Dihedral branched covers of four-manifolds
• On closed 3-braids with unknotting number one
• Rational homology cobordisms of plumbed 3-manifolds
• Using rational homology circles to construct rational homology balls
• The lens space realization problem
• A survey of the homology cobordism group
• Rational cobordisms and integral homology
• Slice Implies Mutant Ribbon for Odd, 5-Stranded Pretzel Knots
• A construction of slice knots via annulus twists
• Embedding 3-manifolds in spin 4-manifolds
• Branched covers bounding rational homology balls
• Extending fibrations on knot complements to ribbon disk complements
• Surgeries on torus knots, rational balls, and cabling
• Obstructing Sliceness in a Family of Montesinos Knots
• Classification of torus bundles that bound rational homology circles
• Fibered knots with the same $0$-surgery and the slice-ribbon conjecture
• Ribbon cobordisms between lens spaces
• On slice alternating 3-braid closures
• An infinite family of counterexamples to Batson's conjecture
• The Goeritz matrix and signature of a two bridge knot
• On the Slice-Ribbon Conjecture for Montesinos knots
• Cosmetic surgery and the $SL(2,\mathbb{C})$ Casson invariant for two-bridge knots
• The signature of an even symmetric form with vanishing associated linking form
• Nullification of knots and links
• On knots that divide ribbon knotted surfaces
• Stabilizing Four-Torsion in Classical Knot Concordance
• Non-slice 3-stranded pretzel knots
• Equivariantly slicing strongly negative amphichiral knots
• Embedding lens spaces in definite 4-manifolds
• On lens spaces bounding smooth 4-manifolds with ${\mathbf{b}}_2=1$
• Shadows and quantum invariants
• Surgical distance between lens spaces