Abstract
In 1997, T Cochran, K Orr, and P Teichner [Ann. of Math. (2) 157 (2003) 433-519] defined a filtration of the classical knot concordance group ,
The filtration is important because of its strong connection to the classification of topological –manifolds. Here we introduce new techniques for studying and use them to prove that, for each , the group has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson–Gordon and Gilmer, contain slice knots.
Citation
Tim D Cochran. Shelly Harvey. Constance Leidy. "Knot concordance and higher-order Blanchfield duality." Geom. Topol. 13 (3) 1419 - 1482, 2009. https://doi.org/10.2140/gt.2009.13.1419
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