Lens spaces, rational balls and the ribbon conjecture

By P. Lisca. 2007

133 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0acd1a531a4042df0c51e0c4a8b0e5aabdbc9be1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. J. Greene
2. Ana G. Lecuona
3. Stanislav Jabuka

In Mathematical Physics

1. J. Greene
2. Ana G. Lecuona
3. Stanislav Jabuka

Citations in the corpus

• On the slice-ribbon conjecture for Montesinos knots (2009, methodology): “.2, the matrices Mi are non singular, hence M and QP = −MMt are nonsingular as well. ON THE SLICE-RIBBON CONJECTURE FOR MONTESINOS KNOTS 25 For the reader’s convenience we now include two Lemmas from [Li]. More precisely, Lemma 4.4 corresponds to Lemma 2.5 in [Li], which gives important information ”
• The slice-ribbon conjecture for 3-stranded pretzel knots (2007, methodology): “If instead min{|p|, |q|, |r|} = 1, the resulting P (p, q, r) is a 2-bridge knot, in which case the corollary follows from the work of Lisca [11].”
• Sums of lens spaces bounding rational balls (2007, unknown): “G T ] 1 4 M ay 2 00”
• The lens space realization problem (2010, background): “John Baldwin for sharing the meal of paneer bhurji that kicked o this project, and to him, Cameron Gordon, Matt Hedden, John Luecke, and Jake Rasmussen for helpful conversations. Paolo Lisca’s papers [23, 24] and a lecture by Dusa McDu on her joint work with Felix Schlenk [25] were especially in uen”