2015/04/30 by Peter Feller
Mathematics · #Alexander polynomial #Algebraic Geometry and Number Theory #Botany #Combinatorics #Degree (music) #Generalization #Genus #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Knot (papermaking) #Knot invariant #Knot polynomial #Knot theory #Mathematical analysis #Mathematics #Physics #Polynomial #Pure mathematics #Topology (electrical circuits) #Upper and lower bounds #math.GT #msc:57M25 #msc:57M27
paper · pdf · doi:10.2140/gt.2016.20.1763
published as Geom. Topol. 20 (2016), no. 3, 1763-1771 · 7 pages, 1 figure. Comments welcome! Version 2: Change in convention for the degree of the Alexander polynomial. Accepted for publication by Geometry and Topology
arxiv created 2016/03/29 · openalex publication_date 2016/07/04 · arxiv updated 2017/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We use the famous knot-theoretic consequence of Freedman’s disc theorem — knots with trivial Alexander polynomial bound a locally flat disc in the [math] –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.