Murakami–Przytycki's unknotting-number conjecture for positive fibered knots

Let KK be a positive fibered knot, let u(K)u(K) denote its unknotting number, and let g(K)g(K) denote its Seifert genus.

Murakami–Przytycki's conjecture. For every positive fibered knot KK,

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

The conjecture concerns whether the lower bound supplied by positivity is always sharp for positive fibered knots. The source presents it as a further related conjecture and gives no resolution, so it remains open here.

Sources & referencesView supporting material

Primary source

A. Stoimenow, “Positive knots, closed braids and the Jones polynomial”, arXiv:math/9805078 (2001).

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