Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 60, Number 1 (2016), 179-184.
A knot without a nonorientable essential spanning surface
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.
Illinois J. Math., Volume 60, Number 1 (2016), 179-184.
Received: 23 September 2015
Revised: 9 October 2016
First available in Project Euclid: 21 June 2017
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Dunfield, Nathan M. A knot without a nonorientable essential spanning surface. Illinois J. Math. 60 (2016), no. 1, 179--184. https://projecteuclid.org/euclid.ijm/1498032029