Concordance to links with unknotted components

Details Concordance to links with unknotted components Concordance to links with unknotted components

2011-03-12

arxiv.org/abs/1103.2417v3

Mathematics

Geometric Topology

Final version, to appear in Algebraic & Geometric Topology

Scientific paper

We show that there are links whose individual components are concordant to the unknot, but which are not concordant to any link with unknotted components. We give examples in the topological category, and examples in the smooth category which are topologically slice. We also give generalizations regarding components of prescribed Alexander polynomials. The main tools are covering link calculus, algebraic invariants of rational knot concordance theory, and the correction term of Heegaard Floer homology.

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