Alternating links and definite surfaces

By J. Greene. 2015

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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 Juh\'asz and Lackenby, applies the characterization to derive an exponential time algorithm for alternating knot recognition.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6ea90d171c53dc32a201f16d6e9d3140686e6b0a