Concordance of links with identical Alexander invariants

Abstract

J. Davis showed that the topological concordance class of a link in the 3-sphere is uniquely determined by its Alexander polynomial for 2-component links with Alexander polynomial one. A similar result for knots with Alexander polynomial one was shown earlier by M. Freedman. We prove that these two cases are the only exceptional cases, by showing that the link concordance class is not determined by the Alexander invariants in any other case.

14 pages

References in corpus (5)

• Knot Concordance and Higher-Order Blanchfield Duality
• Higher Order Intersections in Low-Dimensional Topology
• Whitney tower concordance of classical links
• Smooth concordance of links topologically concordant to the Hopf link
• Hidden torsion, 3-manifolds, and homology cobordism

Cited by in corpus (4)

• A topological approach to Cheeger-Gromov universal bounds for von Neumann rho-invariants
• 2-torsion in the grope and solvable filtrations of knots
• Links with nontrivial Alexander polynomial which are topologically concordant to the Hopf link
• Knots having the same Seifert form and primary decomposition of knot concordance