Tags » Hyperbolic Geometry

Teichmüller geometry: a primer

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


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

Problem Solving

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

Hyperbolic Geometry

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

Hyperbolic Geometry

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


SnapPy 2.4 released

A new version of SnapPy, a program for studying the topology and geometry of 3-manifolds, is available.  Added features include a census of Platonic manifolds, rigorous computation of cusp translations, and substantial improvements to its link diagram component.