The slice-ribbon conjecture for 3-stranded pretzel knots

2007/06/24 by Joshua Greene, Greene, Joshua, Stanislav Jabuka +1 · 1 citation
Mathematics · #57M25 #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25 #msc:57M27

paper · pdf · doi:10.48550/arxiv.0706.3398

21 pages, 5 figures. Significantly expanded version, mistake in previous proof corrected

arxiv created 2007/08/07 · arxiv updated 2009/12/01

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.

Cited by

• Smooth concordance of cables of the figure-eight knot

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• Non-slice 3-stranded pretzel knots
• Distinguishing mutant pretzel knots in concordance
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