A counterexample to Question 1 of "A survey on the Turaev genus of knots"

Cody Armond; Moshe Cohen

doi:10.1090/proc/12842

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arXiv · 1407.3259

A counterexample to Question 1 of "A survey on the Turaev genus of knots"

Cody Armond·Moshe Cohen

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Abstract

In "A survey on the Turaev genus of knots," Champanerkar and Kofman propose several open questions. The first asks whether the polynomial whose coefficients count the number of quasi-trees of the all-A ribbon graph obtained from a diagram with minimal Turaev genus is an invariant of the knot. We answer negatively by showing a counterexample obtained from the two diagrams of $8_{21}$ on the KnotAtlas and KnotScape.

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Cody Armond, Moshe Cohen. 2014-07-11. A counterexample to Question 1 of "A survey on the Turaev genus of knots". https://doi.org/10.1090/proc/12842

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