Journal title
Duke Mathematical Journal
DOI
10.1215/00127094-2017-0004
Issue
11
Volume
166
Last updated
2024-04-07T19:05:32.147+01:00
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
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Publication type
Journal Article
Publication date
05 May 2017