Riemann surfaces and AF-algebras

Abstract

For a generic set in the Teichmüller space, we construct a covariant functor with the range in a category of the $\mathit{AF}$-algebras; the functor maps isomorphic Riemann surfaces to the stably isomorphic $\mathit{AF}$-algebras. In the special case of genus one, one gets a functor between the category of complex tori and the Effros–Shen algebras.