The graded count of quasi-trees is not a knot invariant
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 ans...
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Veröffentlicht in: | Proceedings of the American Mathematical Society 2016-05, Vol.144 (5), p.2285-2290 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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 8218_{21} on the Knot Atlas and KnotScape. |
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ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/proc/12842 |