Infinite-dimensional Teichmüller spaces and modular groups

Abstract

In this chapter, we give a synthetic treatment concerning recent theories on the dynamics of Teichmüller modular groups for Riemann surfaces of infinite topological type. We consider quotient spaces of the Teichmüller space by subgroups of the modular group in order to find a moduli space in an appropriate sense. Among a glossary of fundamental results on this subject matter, we emphasize the construction of the stable moduli space and the enlarged moduli space, both of which are regarded as generalizations of the concept of moduli spaces from finite type Riemann surfaces to infinite type surfaces.