The genus *g* Teichmüller space Teich(*g*) is the space of all marked hyperbolic metrics on a genus *g* surface , modulo homotopy, or equivalently the space of all conformal structures, modulo biholomorphisms isotopic to the identity. 1,060 more words

## Tags » Hyperbolic Geometry

#### Teichmüller geometry: a primer

#### Hyperbolic Plane Example

Few months ago I gave a lecture on Non-euclidean geometry and it was a bit difficult for me to give audience an example of hyperbolic surface from their day-to-day life. 236 more words

#### Isomorphic groups via hyperbolic geometry

is the isometry group of hyperbolic 2-space under the hyperboloid model; is the isometry group of the upper half-plane; is the isometry group of the Poincaré unit disk. 58 more words

#### Mostow Rigidity: several proofs

**Mostow rigidity** (or, technically, the special case thereof, for , states that if *M* and *N* are two closed (i.e. compact and boundary-less) hyperbolic 3-manifolds, and is a homotopy equivalence. 1,185 more words

#### Arguments using moduli spaces: some examples

This blogpost started as a response to the question “why moduli spaces?” … but then David Ben-Zvi had a good pithy answer to that in his 2,288 more words