Alternating links and definite surfaces

Author: 

Greene, J

Publication Date: 

5 May 2017

Journal: 

Duke Mathematical Journal

Last Updated: 

2020-03-10T16:28:08.983+00:00

Issue: 

11

Volume: 

166

DOI: 

10.1215/00127094-2017-0004

page: 

2133-2151

abstract: 

We establish a characterization of alternating links in terms of definite spanning surfaces. We apply it to obtain a new proof of Tait's conjecture that reduced alternating diagrams of the same link have the same crossing number and writhe. We also deduce a result of Banks and of Hirasawa and Sakuma about Seifert surfaces for special alternating links. The appendix, written by Juhász and Lackenby, applies the characterization to derive an exponential time algorithm for alternating knot recognition.

Symplectic id: 

724741

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article