The author studies complex structures on the compact solenoid from the viewpoint of the complex analytic theory of Teichmüller spaces. He gives different equivalent definitions of the compact solenoid. He summarizes consequences related to the infinitesimal structure of the Teichmüller space. He analyses the extremal maps in a given homotopy class. He constructs two finite index subgroups of the modular group which are conjugated by a quasi-symmetric homeomorphism of the unit circle.
For the entire collection see [Zbl 1158.30001].