Geodesic
On the genus defect of positive braid knots
Liechti, Livio1
1Department of Mathematics, University of Fribourg, Fribourg, Switzerland
Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 403-428
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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.

DOI : 10.2140/agt.2020.20.403
Classification : 57M25, 57M27, 06A06
Keywords: four-genus, genus defect, positive braid knot, surface minor, well-quasiorder

Liechti, Livio  1

1 Department of Mathematics, University of Fribourg, Fribourg, Switzerland 
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Liechti, Livio. On the genus defect of positive braid knots. Algebraic and Geometric Topology, Tome 20 (2020) no. 1, pp. 403-428. doi: 10.2140/agt.2020.20.403

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