Every lens space contains a genus one homologically fibered knot

Yuta Nozaki

doi:10.1215/ijm/1552442658

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arXiv · 1702.02731

Every lens space contains a genus one homologically fibered knot

Yuta Nozaki

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Abstract

We prove that every lens space contains a genus one homologically fibered knot, which is contrast to the fact that some lens spaces contain no genus one fibered knot. In the proof, the Chebotarev density theorem and binary quadratic forms in number theory play a key role. We also discuss the Alexander polynomial of homologically fibered knots.

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Yuta Nozaki. 2017-02-09. Every lens space contains a genus one homologically fibered knot. https://doi.org/10.1215/ijm/1552442658

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