Plumbing coordinates on Teichmüller space: A counterexample

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 ...

Bijective Mappings with Generalized Barycentric Coordinates: A Counterexample

Many recent works attempt to generalize barycentric coordinates to arbitrary polygons. I construct a counterexample proving that no such generalization will produce purely bijective mappings in the plane provided the coordinates meet the Lagrange, reproduction, and partition of unity properties. The proof concerns generalized barycentric coordinates in a square, but trivially generalizes to arb...

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...