Student Geometry/Topology Seminar

Topological coverings of surfaces induce embeddings of their Teichmüller spaces. One might ask what happens if we repeat this construction through an infinite tower of covers. The universal hyperbolic solenoid results, and is an interesting object both on its own and for some applications. The solenoid can be endowed with complex structures, and has an infinite-dimensional Teichmüller space which contains the Teichmüller spaces of all closed surfaces. In this talk, we will introduce the solenoid and describe a few aspects of its Teichmüller space, noticing some interesting comparisons with the case of finite-type surfaces. Speaker(s): Mark Greenfield (University of Michigan)