Category: Topology

Geogebra model for hyperbolic isometries
The goals of this GeoGebra model are the following: 1) Input a hyperbolic isometry of the hyperbolic plane using the matrix representation. In other words input a real matrix with determinant 1 and trace more than 2. 2) Programmatically draw the axis. 3) Mark any point P on the hyperbolic plane (upper half plane) 4)…

Which manifold is this?
This is the first exercise from Thurston’s Three Dimensional Geometry and Topology Vol. 1. Which manifold is this? It is like an old trick. Try following the lines. There are actually 6 loops (circles) in this maze. Here is a color coded picture of it.