The Teichmüller space of an arbitrary Fuchsian group

Quantum Teichmüller Space

We describe explicitly a noncommutative deformation of the *-algebra of functions on the Teichmüller space of Riemann surfaces with holes equivariant w.r.t. the mapping class group action.

Dynamics over Teichmüller Space

Fuzzy Subgroups and the Teichmüller Space

There exists a generalization of the Teichmüller space of a covering group. In this paper we combine this generalized Teichmüller space T (G) and any fuzzy subgroup A : G−→ F where G is a subgroup of the group consisting of such orientation preserving and orientation reversing Möbius transformations which act in the upper half-plane of the extended complex plane. A partially ordered set F = (F ...

Coordinates for Quasi-Fuchsian Punctured Torus Space

We consider complex Fenchel–Nielsen coordinates on the quasi-Fuchsian space of punctured tori. These coordinates arise from a generalisation of Kra’s plumbing construction and are related to earthquakes on Teichmüller space. They also allow us to interpolate between two coordinate systems on Teichmüller space, namely the classical Fuchsian space with Fenchel–Nielsen coordinates and the Maskit e...

Exotic Projective Structures and Quasi-fuchsian Space

1. Introduction. Let S be an oriented closed surface of genus g > 1. A projec-tive structure on S is a maximal system of local coordinates modeled on the Riemann sphere C, whose transition functions are Möbius transformations. For a given pro-jective structure on S, we have a pair (f, ρ) of a local homeomorphism f from the universal cover S of S to C, called a developing map, and a group homomo...