On a Teichmueller functor between the categories of complex tori and the Effros-Shen algebras

TL;DR

This paper constructs a covariant functor linking complex tori and Effros-Shen algebras, utilizing Teichmüller theory to map isomorphic structures between these categories.

Contribution

It introduces a novel functor connecting complex tori with Effros-Shen algebras based on Teichmüller theory, preserving isomorphisms.

Findings

Functor maps isomorphic complex tori to stably isomorphic Effros-Shen algebras

Construction is based on Teichmüller theory of Riemann surfaces

Establishes a categorical relationship between geometric and algebraic structures

Abstract

A covariant functor from the category of the complex tori to the category of the Effros-Shen algebras is constructed. The functor maps isomorphic complex tori to the stably isomorphic Effros-Shen algebras. Our construction is based on the Teichmueller theory of the Riemann surfaces.