Note on character varieties and cluster algebras

研究成果: Contribution to journalArticle査読

1 被引用数 (Scopus)

抄録

We use Bonahon-Wong’s trace map to study character varieties of the oncepunctured torus and of the 4-punctured sphere. We clarify a relationship with cluster algebra associated with ideal triangulations of surfaces, and we show that the Goldman Poisson algebra of loops on surfaces is recovered from the Poisson structure of cluster algebra. It is also shown that cluster mutations give the automorphism of the character varieties. Motivated by a work of Chekhov-Mazzocco-Rubtsov, we revisit con uences of punctures on sphere from cluster algebraic viewpoint, and we obtain associated affine cubic surfaces constructed by van der Put-Saito based on the Riemann-Hilbert correspondence. Further studied are quantizations of character varieties by use of quantum cluster algebra.

本文言語英語
論文番号003
ジャーナルSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
15
DOI
出版ステータス出版済み - 2019

All Science Journal Classification (ASJC) codes

  • 分析
  • 数理物理学
  • 幾何学とトポロジー

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