Stoimenow's unknotting-number conjecture for positive fibered knots

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Let KK be a positive fibered knot. Its unknotting number is denoted by u(K)u(K), and its 3-genus by g(K)g(K). Stoimenow's conjecture.

u(K)=g(K).u(K)=g(K).

The conjecture extends the equality known for braid-positive knots. The paper disproves the conjecture by exhibiting a positive fibered knot whose unknotting number exceeds its genus.

References

Primary source

Marc Kegel, Lukas Lewark, Naageswaran Manikandan, Filip Misev, Leo Mousseau and Marithania Silvero, “On unknotting fibered positive knots and braids”, arXiv:2312.07339 (2024).

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