Knot concordance and higher-order Blanchfield duality

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Abstract

In 1997, T Cochran, K Orr, and P Teichner [Ann. of Math. (2) 157 (2003) 433519] defined a filtration of the classical knot concordance group C, The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each n in N0, the group Fn/Fn.5 has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a longstanding question as to whether certain natural families of knots, first considered by Casson-Gordon and Gilmer, contain slice knots. © 2009 Mathematical Sciences Publishers.

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Cochran, T. D., Harvey, S., & Leidy, C. (2009). Knot concordance and higher-order Blanchfield duality. Geometry and Topology, 13(3), 1419–1482. https://doi.org/10.2140/gt.2009.13.1419

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