Integrable 3D Statistical Models on Six-Valent Graphs

Integrable 3D Statistical Models on Six-Valent Graphs

The paper is devoted to the study of a special statistical model on graphs with vertices of degrees 6 and 1. We show that this model is invariant with respect to certain Roseman moves if one regards the graph as the singular point set of the diagram of a 2-knot. Our approach is based on the properti...

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Veröffentlicht in:Proceedings of the Steklov Institute of Mathematics 2018-08, Vol.302 (1), p.198-216
Hauptverfasser: Korepanov, I. G., Talalaev, D. V., Sharygin, G. I.
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graphs
Mathematics
Mathematics and Statistics
Statistical models
Tetrahedra
Three dimensional models
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Beschreibung
Zusammenfassung:The paper is devoted to the study of a special statistical model on graphs with vertices of degrees 6 and 1. We show that this model is invariant with respect to certain Roseman moves if one regards the graph as the singular point set of the diagram of a 2-knot. Our approach is based on the properties of the tetrahedron cohomology complex.
ISSN:0081-5438
1531-8605
DOI:10.1134/S008154381806010X