Concordance to links with unknotted components
Jae Choon Cha, Daniel Ruberman
TL;DR
This paper investigates the subtle differences in link concordance, showing that some links with unknotted components are not concordant to links with all unknotted components, using advanced topological and algebraic tools.
Contribution
It provides new examples and generalizations in link concordance, highlighting distinctions between topological and smooth categories with novel invariants.
Findings
Existence of links with unknotted components not concordant to any with all unknotted components
Examples in both topological and smooth categories, including topologically slice links
Use of covering link calculus, algebraic invariants, and Heegaard Floer correction terms
Abstract
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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