A knot without a nonorientable essential spanning surface

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This note gives the first example of a hyperbolic knot in the 3-sphere that lacks a nonorientable essential spanning surface; this disproves the Strong Neuwirth Conjecture formulated by Ozawa and Rubinstein. Moreover, this knot has no even strict boundary slopes, disproving the Even Boundary Slope Conjecture of the same authors. The proof is a rigorous calculation using Thurston’s spun-normal surfaces in the spirit of Haken’s original normal surface algorithms.

Original languageEnglish (US)
Pages (from-to)179-184
Number of pages6
JournalIllinois Journal of Mathematics
Issue number1
StatePublished - 2016

ASJC Scopus subject areas

  • General Mathematics


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