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Upper bounds for the topological slice genus of knots (Feller/Lewark)

Banff International Research Station for Mathematical Innovation and Discovery

In 1981, Freedman proved that knots with trivial Alexander polynomial bound a locally flat disc in the four-ball. As a consequence, the degree of the Alexander polynomial constitutes an upper bound for the topological slice genus of a knot (F., 2015). We discuss a stronger bound, which is still determined solely by the knot's Seifert form. As sample applications, we will see upper bounds for the slice genus of torus knots (Baader, F., L., Liechti) and two-bridge knots (F., Mccoy), and for the stable slice genus of alternating knots (Baader, L.)."

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: Universität Bern

2016-08-24

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58964

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/