Geometry & Topology
- Geom. Topol.
- Volume 20, Number 3 (2016), 1763-1771.
The degree of the Alexander polynomial is an upper bound for the topological slice genus
We use the famous knot-theoretic consequence of Freedman’s disc theorem — knots with trivial Alexander polynomial bound a locally flat disc in the –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.
Geom. Topol., Volume 20, Number 3 (2016), 1763-1771.
Received: 13 April 2015
Revised: 4 September 2015
Accepted: 6 September 2015
First available in Project Euclid: 16 November 2017
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Feller, Peter. The degree of the Alexander polynomial is an upper bound for the topological slice genus. Geom. Topol. 20 (2016), no. 3, 1763--1771. doi:10.2140/gt.2016.20.1763. https://projecteuclid.org/euclid.gt/1510859002