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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Proceedings of the American Mathematical Society 2016-05, Vol.144 (5), p.2285-2290
Hauptverfasser: Armond, Cody, Cohen, Moshe
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/12842