Knot Concordance and Higher-Order Blanchfield Duality

Details Knot Concordance and Higher-Order Blanchfield Duality Knot Concordance and Higher-Order Blanchfield Duality

2007-10-16

arxiv.org/abs/0710.3082v3

Geometry and Topology, 13 (2009), 1419-1482

Mathematics

Geometric Topology

Corrected Figure in Example 8.4, Added Remark 5.11 pointing out an important strengthening of Theorem 5.9 that is needed in a

Scientific paper

10.2140/gt.2009.13.1419

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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