The graded count of quasi-trees is not a knot invariant

Armond, Cody; Cohen, Moshe

doi:10.1090/proc/12842

The graded count of quasi-trees is not a knot invariant
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by Cody Armond and Moshe Cohen PDF

Proc. Amer. Math. Soc. 144 (2016), 2285-2290 Request permission

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 Knot Atlas and KnotScape.

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