Knot concordance and higher-order Blanchfield duality

By Tim D. Cochran, Shelly L. Harvey, Constance Leidy. 2007

74 citations recorded by the source corpus.

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 n2 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 long-standing question as to whether certain natural families of knots, first considered by Casson‐Gordon and Gilmer, contain slice knots. 57M25; 57M10

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ed97f5517899ac8c0b7fe9586c3b46b06bde04eb

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Primary decomposition and the fractal nature of knot concordance (2009, background): “Then varying J over any collection of Arf invariant zero knots with independent signatures yields an infinite family generating Z∞ ⊂ G2 [16].”
Topologically slice knots with nontrivial Alexander polynomial (2010, background): “5 for all i was proved in [5] (see also [10] for the existence of elements of infinite order in each of the quotients).”
Metabelian representations, twisted Alexander polynomials, knot slicing, and mutation (2008, unknown): “A few more recent articles include [4,5,9,32,34,35].”