Manchester Geometry Seminar 2002/2003

In investigating the problem of identifying 3-dimensional hyperbolic manifolds and, more particularly, orbifolds of small volume, many Kleinian groups with two generators of finite order arise. Such groups also arise in the context of carrying out orbifold surgery on knot and link complements and in several other contexts. Many of these groups turn out to be arithmetic and in joint work with Gaven Martin, I have embarked on a project to identify all such arithmetic groups. This talk will discuss the background to this and progress on the project.