Decorated enhanced Teichm\"uller spaces

Abstract

In this paper, we introduce a new variation of the Teichm\"{u}ller space, namely the deformation space of hyperbolic structures on a surface with both enhancement and decoration. We construct the parameterization of this deformation space, which is a common generalization of the shear coordinates and the $\lambda$-length coordinates. Furthermore, we introduce the lamination space corresponding to this deformation space, and show the compatibility of the shear coordinates and the $\lambda$-length coordinates.