Faculté des sciences et de médecine

On the genus defect of positive braid knots

Liechti, Livio

In: Algebraic & Geometric Topology, 2020, vol. 20, no. 1, p. 403–428

We show that the difference between the Seifert genus and the topological 4–genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive braid representatives of the knot. We deduce that among prime positive braid knots, the property of having such a genus difference less than any fixed constant is characterised by finitely... More

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    Summary
    We show that the difference between the Seifert genus and the topological 4–genus of a prime positive braid knot is bounded from below by an affine function of the minimal number of strands among positive braid representatives of the knot. We deduce that among prime positive braid knots, the property of having such a genus difference less than any fixed constant is characterised by finitely many forbidden surface minors.