Stoimenow's unknotting-number conjecture for positive fibered knots

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.

Sources & referencesView supporting material

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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