Moduli of complex curves and noncommutative geometry I: Riemann surfaces and dimension groups
نویسنده
چکیده
This paper is a brief account of the moduli of complex curves from the perspective of noncommutative geometry. We focus on the uniformization of Riemann surfaces by the ordered K-groups of a noncommutative C-algebra. Using this approach, we prove “generic” arithmeticity of the mapping class group and study correspondences between complex and noncommutative tori.
منابع مشابه
Moduli of complex curves and noncommutative geometry: Riemann surfaces and dimension groups
This paper is a brief account of the moduli of complex curves from the perspective of noncommutative geometry. Using a uniformization of Riemann surfaces by the ordered abelian groups, we prove that modulo the Torelli group, the mapping class group of surface of genus g with n holes, is linear arithmetic group of rank 6g − 6 + 2n.
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