The Roger–Yang skein algebra and the decorated 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 ...

Cell Decomposition and Compactification of Riemann's Moduli Space in Decorated Teichmüller Theory

This survey covers earlier work of the author as well as recent work on Riemann's moduli space, its canonical cell decomposition and compactification, and the related operadic structure of arc complexes.

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.

Skein algebra of a group

We define for each group G the skein algebra of G. We show how it is related to the Kauffman bracket skein modules. We prove that skein algebras of abelian groups are isomorphic to symmetric subalgebras of corresponding group rings. Moreover, we show that, for any abelian group G, homomorphisms from the skein algebra of G to C correspond exactly to traces of SL(2, C)-representations of G. We al...

Dynamics over Teichmüller Space