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Note on character varieties and cluster algebras. (arXiv:1711.03379v1 [math-ph])
来源于:arXiv
We use Bonahon-Wong's trace map to study character varieties of
once-punctured torus and of 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 automorphism of character varieties. Motivated by a work of Chekhov,
Mazzocco & Rubtsov, we revisit confluences 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. 查看全文>>