Geometry & Topology

Knot concordance and higher-order Blanchfield duality

Tim D Cochran, Shelly Harvey, and Constance Leidy

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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 C,

n 1 0 . 5 0 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 n0, the group nn.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.

Article information

Geom. Topol., Volume 13, Number 3 (2009), 1419-1482.

Received: 10 September 2008
Accepted: 1 December 2008
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M10: Covering spaces

concordance (n)-solvable knot slice knot Blanchfield form von Neumann signature


Cochran, Tim D; Harvey, Shelly; Leidy, Constance. Knot concordance and higher-order Blanchfield duality. Geom. Topol. 13 (2009), no. 3, 1419--1482. doi:10.2140/gt.2009.13.1419.

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