A remark on the counterexample to the unknotting number conjecture

By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$, where $7_1$ is the $(2,7)$-torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact.

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Publication Details

Journal
ArXiv.org
Published
2025-07-18
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

A remark on the counterexample to the unknotting number conjecture

Yimu Zhang, Chao Wang
ArXiv.org
Algebraic Geometry and Number Theory
article

A remark on the counterexample to the unknotting number conjecture

Yimu Zhang, Chao Wang
article en

Abstract

By using Snappy, M. Brittenham and S. Hermiller discovered a very surprising example that $u(7_1\#\overline{7_1})\leq 5<6=u(7_1)+u(\overline{7_1})$, where $7_1$ is the $(2,7)$-torus knot and $\overline{7_1}$ is its mirror image. Based on their work, we give a direct verification of this fact.

ArXiv.org
Openalex Percentile: Top 57%
Algebraic Geometry and Number Theory
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A remark on the counterexample to the unknotting number conjecture — Yimu Zhang, Chao Wang · ArXiv.org (2025) | TGRS Research Map | TGRS