The Teichmüller space of a countable set of points on a Riemann surface

Abstract

We introduce the quasiconformal deformation space of an ordered countable set of an infinite number of points on a Riemann surface and give certain conditions under which it admits a complex structure via Teichmüller spaces of associated subsurfaces with the complement of the set of points. In a similar fashion, we give another definition of the quasiconformal deformation space of a finitely generated Kleinian group.