Riemann surfaces and AF-algebras

TL;DR

This paper constructs a functor linking Riemann surfaces to AF-algebras, establishing a categorical correspondence that connects complex tori with Effros-Shen algebras, enriching the interplay between geometry and operator algebras.

Contribution

It introduces a covariant functor from Teichmueller space to AF-algebras, creating a novel categorical link between Riemann surfaces and operator algebras.

Findings

Riemann surfaces are associated with AF-algebras via a covariant functor.

Isomorphic Riemann surfaces correspond to stably isomorphic AF-algebras.

Establishes a categorical correspondence between complex tori and Effros-Shen algebras.

Abstract

For a generic set in the Teichmueller space, we construct a covariant functor with the range in a category of the AF-algebras; the functor maps isomorphic Riemann surfaces to the stably isomorphic AF-algebras. As a special case, one gets a categorical correspondence between complex tori and the so-called Effros-Shen algebras.