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arXiv · 0710.3082

Knot Concordance and Higher-Order Blanchfield Duality

Tim D. Cochran·Shelly Harvey·Constance Leidy
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Abstract

In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} 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 natural number n, the abelian group F_n/F_{n.5} 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.

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Tim D. Cochran, Shelly Harvey, Constance Leidy. 2008-09-14. Knot Concordance and Higher-Order Blanchfield Duality. https://doi.org/10.2140/gt.2009.13.1419

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