Note on Character Varieties and Cluster Algebras

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2019
• 1. Verfasser: Hikami, K.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2019
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/210072
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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...