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Spring 2016 A knot without a nonorientable essential spanning surface
Nathan M. Dunfield
Illinois J. Math. 60(1): 179-184 (Spring 2016). DOI: 10.1215/ijm/1498032029

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.

Citation

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Nathan M. Dunfield. "A knot without a nonorientable essential spanning surface." Illinois J. Math. 60 (1) 179 - 184, Spring 2016. https://doi.org/10.1215/ijm/1498032029

Information

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

zbMATH: 06734368
MathSciNet: MR3665177
Digital Object Identifier: 10.1215/ijm/1498032029

Subjects:
Primary: 57M

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 1 • Spring 2016
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