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15 August 2017 Alternating links and definite surfaces
Joshua Evan Greene
Duke Math. J. 166(11): 2133-2151 (15 August 2017). DOI: 10.1215/00127094-2017-0004

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.

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Joshua Evan Greene. "Alternating links and definite surfaces." Duke Math. J. 166 (11) 2133 - 2151, 15 August 2017. https://doi.org/10.1215/00127094-2017-0004

Information

Received: 26 January 2016; Revised: 21 October 2016; Published: 15 August 2017
First available in Project Euclid: 5 May 2017

zbMATH: 1377.57009
MathSciNet: MR3694566
Digital Object Identifier: 10.1215/00127094-2017-0004

Subjects:
Primary: 57M25
Secondary: 05C21, 05C50, 11H55, 57M15, 57M27

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 11 • 15 August 2017
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