The slice-ribbon conjecture for 3-stranded pretzel knots
By J. Greene, Stanislav Jabuka. 2007
74 citations recorded by the source corpus.
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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a576e143d428d40382a89afb8a3eebb1decf8f41
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In Discrete Mathematics and Combinatorics
- Shelly L. Harvey
- Tim D. Cochran
- John A. Baldwin
- Peter D. Horn
- Jae Choon Cha
- Stefan Friedl
- P. Teichner
- Stefano Vidussi
In Geometry and Topology
- Shelly L. Harvey
- Tim D. Cochran
- John A. Baldwin
- Peter D. Horn
- Jae Choon Cha
- Stefan Friedl
- Constance Leidy
- P. Teichner
In Mathematical Physics
- Shelly L. Harvey
- Tim D. Cochran
- John A. Baldwin
- Peter D. Horn
- Jae Choon Cha
- Stefan Friedl
- Constance Leidy
- P. Teichner
Citations in the corpus
- Filtering smooth concordance classes of topologically slice knots (2012, background): “Various authors have observed that this line of thinking leads to the meta-statement: d-invariants of prime-power branched covers obstruct being a slice knot [42, 30, 38, 29].”
- Heegaard Floer homology and genus one, one‐boundary component open books (2008, background): “One might hope to use these correction terms as in [18, 9] to obtain finer concordance information about K than what is provided here by δ.”
- The lens space realization problem (2010, unknown): “[22], [25]).”