Smooth concordance of links topologically concordant to the Hopf link
Jae Choon Cha, Taehee Kim, Daniel Ruberman, and Saso Strle
TL;DR
This paper demonstrates the existence of 2-component links with Alexander polynomial one that are topologically but not smoothly concordant to the Hopf link, constructing infinitely many such classes and exploring their properties.
Contribution
It provides the first examples of links with Alexander polynomial one that are topologically but not smoothly concordant to the Hopf link, answering a longstanding question.
Findings
Existence of links with Alexander polynomial one not smoothly concordant to the Hopf link
Construction of infinitely many such concordance classes
Links with unknotted components not smoothly concordant even with knots tied in
Abstract
It was shown by Jim Davis that a 2-component link with Alexander polynomial one is topologically concordant to the Hopf link. In this paper, we show that there is a 2-component link with Alexander polynomial one that has unknotted components and is not smoothly concordant to the Hopf link, answering a question of Jim Davis. We construct infinitely many concordance classes of such links, and show that they have the stronger property of not being smoothly concordant to the Hopf link with knots tied in the components.
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