Alternating links and definite surfaces

  title={Alternating links and definite surfaces},
  author={Joshua Evan Greene},
  journal={Duke Mathematical Journal},
  • J. Greene
  • Published 19 November 2015
  • Mathematics
  • Duke Mathematical Journal
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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