Crickets, zippers and the Bers universal Teichmüller space

Drawing Bers Embeddings of the Teichmüller Space of Once-Punctured Tori

We present a computer-oriented method of producing pictures of Bers embeddings of the Teichmüller space of once-punctured tori. The coordinate plane is chosen in such a way that the accessory parameter is hidden in the relative position of the origin. Our algorithm consists of two steps. To each point in the coordinate plane, we first compute the corresponding monodromy representation by numeri...

On the Tangent Space to the Universal Teichmüller Space Subhashis Nag

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space : (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The complex-analytic model comprising 1-parameter families of schlicht functions on the exterior of the unit disc which allow quasiconformal extension. Indeed, the Fourier...

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.

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 ...

Dynamics over Teichmüller Space