Concordance of links with identical Alexander invariants
Copyright policy )Concordance of links with identical Alexander invariants
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
- Durham University United Kingdom
- University of Regensburg Germany
- Pohang University of Science and Technology Korea (Republic of)
- UNIVERSITE DE MONTREAL Canada
- Indiana University United States
knots, Geometric Topology (math.GT), 57M25, 57M27, 57N70, GROPES, HOMOLOGY COBORDISM, Invariants of knots and \(3\)-manifolds, TOPOLOGICALLY SLICE-KNOTS, Alexander polynomial, HOPF LINK, topological concordance class, Mathematics - Geometric Topology, Cobordism and concordance in topological manifolds, WHITNEY TOWERS, KNOT CONCORDANCE, Alexander invariants, SMOOTH CONCORDANCE, MANIFOLDS, L-2-SIGNATURES, FOS: Mathematics, Knots and links in the \(3\)-sphere, 2-COMPONENT LINK
knots, Geometric Topology (math.GT), 57M25, 57M27, 57N70, GROPES, HOMOLOGY COBORDISM, Invariants of knots and \(3\)-manifolds, TOPOLOGICALLY SLICE-KNOTS, Alexander polynomial, HOPF LINK, topological concordance class, Mathematics - Geometric Topology, Cobordism and concordance in topological manifolds, WHITNEY TOWERS, KNOT CONCORDANCE, Alexander invariants, SMOOTH CONCORDANCE, MANIFOLDS, L-2-SIGNATURES, FOS: Mathematics, Knots and links in the \(3\)-sphere, 2-COMPONENT LINK
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