Mathematics > Geometric Topology
[Submitted on 4 Apr 2015 (v1), last revised 29 Mar 2016 (this version, v2)]
Title:The degree of the Alexander polynomial is an upper bound for the topological slice genus
View PDFAbstract: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.
Submission history
From: Peter Feller [view email][v1] Sat, 4 Apr 2015 22:38:01 UTC (18 KB)
[v2] Tue, 29 Mar 2016 22:46:39 UTC (18 KB)
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