Oriented Closed Polyhedral Maps and the Kitaev Model

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Author: Szlachányi, Kornél
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212259
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Oriented Closed Polyhedral Maps and the Kitaev Model. Kornél Szlachányi. SIGMA 20 (2024), 048, 55 pages

A kind of combinatorial map, called arrow presentation, is proposed to encode the data of the oriented closed polyhedral complexes Σ on which the Hopf algebraic Kitaev model lives. We develop a theory of arrow presentations which underlines the role of the dual of the double (Σ)* of Σ as being the S...