Hyperbolicity in 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

Statistical Hyperbolicity in Teichmüller Space

In this paper we explore the idea that Teichmüller space with the Teichmüller metric is hyperbolic “on average.” We consider several different measures on Teichmüller space and show that with respect to each one, the average distance between points in a ball of radius r is asymptotic to 2r, which is as large as possible.

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 ...

Generalised Hyperbolicity in Singular Space-times

A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here " curve integrable " are globally hyperbolic in this new sense, and a plausibility argument is given suggesting that the result applies to shell crossing singularities. If the assumptions behind this last argument are valid, this provides an alternative route to the ...