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The slice-ribbon conjecture for 3-stranded pretzel knots

From: American Journal of Mathematics
Volume 133, Number 3, June 2011
pp. 555-580 | 10.1353/ajm.2011.0022

Abstract

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.