Alternating links and definite surfaces

Joshua Evan Greene

doi:10.1215/00127094-2017-0004

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arXiv · 1511.06329

Alternating links and definite surfaces

Joshua Evan Greene

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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 Hirasawa-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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BibTeX RIS

Joshua Evan Greene. 2015-11-19. Alternating links and definite surfaces. https://doi.org/10.1215/00127094-2017-0004

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