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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The degree of the Alexander polynomial is an upper bound for the topological slice genus

Peter Feller

Geometry & Topology 20 (2016) 1763–1771
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.

Keywords
topological slice genus, Alexander polynomial
Mathematical Subject Classification 2010
Primary: 57M25, 57M27
References
Publication
Received: 13 April 2015
Revised: 4 September 2015
Accepted: 6 September 2015
Published: 4 July 2016
Proposed: Dmitri Burago
Seconded: Ciprian Manolescu, Ronald Stern
Authors
Peter Feller
Department of Mathematics
Boston College
Maloney Hall
Chestnut Hill, MA 02467
United States