Rigidity of Teichmüller space

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 ...

Mathematisches Forschungsinstitut Oberwolfach Teichmüller Space (classical and Quantum)

This is a short report on the conference “Teichmüller Space (Classical and Quantum) ” held in Oberwolfach from May 28th to June 3rd, 2006. Mathematics Subject Classification (2000): 32G15; 30F60; 30C62; 57M50; 57N16; 53A35; 30F45; 14H15; 32G81; 81T40; 57R56; 55R40; 20J06; 57N05; 57M99; 57M60; 14H10; 14H15; 14H60; 14N35; 30F30; 30C35; 20F65; 20B25; 53D50; 53C15; 58D29. Introduction by the Organi...

Teichmüller Shape Space Theory and Its Application to Brain Morphometry

Here we propose a novel method to compute Teichmiiller shape space based shape index to study brain morphometry. Such a shape index is intrinsic, and invariant under conformal transformations, rigid motions and scaling. We conformally map a genus-zero open boundary surface to the Poincaré disk with the Yamabe flow method. The shape indices that we compute are the lengths of a special set of geo...