Tags » Hyperbolic Geometry

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

Snippets

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   2,278 more words

Hyperbolic Geometry

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.

3-manifolds

Ergodicity of the Geodesic Flow

The geodesic flow

Given any Riemannian manifold M, we may define a geodesic flow  on the unit tangent bundle which sends a point  1,058 more words

Hyperbolic Geometry

Hyperbolic Geometry Note #2: On Möbius transformations as isometries of the upper half plane

Möbius transformations are conformal (i.e., angle-preserving), orientation-preserving, area-preserving isometries in the upper half-plane model of hyperbolic space. It piqued my interest to discover that the form of the metric in this model (which I discussed in… 732 more words

Hyperbolic Geometry