Illinois Journal of Mathematics

A knot without a nonorientable essential spanning surface

Nathan M. Dunfield

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Abstract

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.

Article information

Source
Illinois J. Math., Volume 60, Number 1 (2016), 179-184.

Dates
Received: 23 September 2015
Revised: 9 October 2016
First available in Project Euclid: 21 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1498032029

Mathematical Reviews number (MathSciNet)
MR3665177

Zentralblatt MATH identifier
06734368

Subjects
Primary: 57M

Citation

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


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