Note on Character Varieties and Cluster Algebras

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2019
• Main Author: Hikami, K.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2019
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/210072
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Note on Character Varieties and Cluster Algebras / K. Hikami // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 50 назв. — англ.

We use Bonahon-Wong's trace map to study character varieties of the once-punctured torus and of the 4-punctured sphere. We clarify a relationship with the cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recov...