Open AccessThe slice-ribbon conjecture for 3-stranded pretzel knots
Author(s) -
Joshua Evan Greene,
Stanislav Jabuka
Publication year - 2011
Publication title -
american journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.818
H-Index - 67
eISSN - 1080-6377
pISSN - 0002-9327
DOI - 10.1353/ajm.2011.0022
Subject(s) - ribbon , mathematics , conjecture , mathematical proof , combinatorics , order (exchange) , pure mathematics , geometry , finance , economics
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.
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