Smooth concordance of links topologically concordant to the Hopf link

Details Smooth concordance of links topologically concordant to the Hopf link Smooth concordance of links topologically concordant to the Hopf link

2010-12-09

arxiv.org/abs/1012.2045v1

Mathematics

Geometric Topology

8 pages, 5 figures

Scientific paper

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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