Liechti, Livio 2020-02-23 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. application/pdf https://folia.unifr.ch/global/documents/308590 https://folia.unifr.ch/documents/308590/files/lie_gdp.pdf eng info:eu-repo/semantics/altIdentifier/doi/10.2140/agt.2020.20.403 info:eu-repo/semantics/openAccess License undefined Algebraic & Geometric Topology. - 2020, vol. 20, no. 1, p. 403–428 info:eu-repo/classification/udc/51 On the genus defect of positive braid knots http://purl.org/coar/resource_type/c_6501