Feller, Peter The degree of the Alexander polynomial is an upper bound for the topological slice genus. (English) Zbl 1386.57008 Geom. Topol. 20, No. 3, 1763-1771 (2016). Summary: We use the famous knot-theoretic consequence of Freedman’s disc theorem – knots with trivial Alexander polynomial bound a locally flat disc in the \(4\)-ball – to prove the following generalization: the degree of the Alexander polynomial of a knot is an upper bound for twice its topological slice genus. We provide examples of knots where this determines the topological slice genus. Cited in 9 Documents MSC: 57M25 Knots and links in the \(3\)-sphere (MSC2010) 57M27 Invariants of knots and \(3\)-manifolds (MSC2010) Keywords:topological slice genus; Alexander polynomial PDFBibTeX XMLCite \textit{P. Feller}, Geom. Topol. 20, No. 3, 1763--1771 (2016; Zbl 1386.57008) Full Text: DOI arXiv