## Geometry & Topology

### The degree of the Alexander polynomial is an upper bound for the topological slice genus

Peter Feller

#### Abstract

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.

#### Article information

Source
Geom. Topol., Volume 20, Number 3 (2016), 1763-1771.

Dates
Revised: 4 September 2015
Accepted: 6 September 2015
First available in Project Euclid: 16 November 2017

https://projecteuclid.org/euclid.gt/1510859002

Digital Object Identifier
doi:10.2140/gt.2016.20.1763

Mathematical Reviews number (MathSciNet)
MR3523068

Zentralblatt MATH identifier
06624258

#### Citation

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

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