Translator Disclaimer
2016 The degree of the Alexander polynomial is an upper bound for the topological slice genus
Peter Feller
Geom. Topol. 20(3): 1763-1771 (2016). DOI: 10.2140/gt.2016.20.1763

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.

Citation

Download Citation

Peter Feller. "The degree of the Alexander polynomial is an upper bound for the topological slice genus." Geom. Topol. 20 (3) 1763 - 1771, 2016. https://doi.org/10.2140/gt.2016.20.1763

Information

Received: 13 April 2015; Revised: 4 September 2015; Accepted: 6 September 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06624258
MathSciNet: MR3523068
Digital Object Identifier: 10.2140/gt.2016.20.1763

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
9 PAGES


SHARE
Vol.20 • No. 3 • 2016
MSP
Back to Top