# Alternating links and definite surfaces

@article{Greene2017AlternatingLA, title={Alternating links and definite surfaces}, author={Joshua Evan Greene}, journal={Duke Mathematical Journal}, year={2017}, volume={166}, pages={2133-2151} }

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.

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