Riemann surfaces: noncommutative story
نویسنده
چکیده
For an open and dense subset in the Teichmüller space, we introduce a coordinate system which is (relatively) well-behaved under the action of the mapping class group. Surprisingly, the coordinates involve the set of projections and traces in a C∗-algebra. We argue that our approach might be helpful for representation of the mapping class group, and other issues.
منابع مشابه
Moduli of complex curves and noncommutative geometry I: Riemann surfaces and dimension groups
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.
متن کاملModuli 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.
متن کاملOn a Teichmüller functor between the categories of complex and noncommutative tori
A covariant functor from category of complex tori to the category of noncommutative tori is constructed. The functor maps isomorphic complex tori to the Morita equivalent noncommutative tori. Our construction is based on the Teichmüller theory of Riemann surfaces.
متن کاملOn complex and noncommutative tori
The “noncommutative geometry” of complex algebraic curves is studied. As first step, we clarify a morphism between elliptic curves, or complex tori, and C-algebras Tθ = {u, v | vu = e2πiθuv}, or noncommutative tori. The main result says that under the morphism isomorphic elliptic curves map to the Morita equivalent noncommutative tori. Our approach is based on the rigidity of the length spectra...
متن کاملQuantum Teichmüller Space
We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008