Geometric manifolds are spaces in which one can do geometry locally, where "geometry" is interpreted in a suitable way. Coxeter groups are an abstract generalisation of groups generated by reflections that arise classically. I will give a brief survey of some of the questions one might want to ask about geometric manifolds, and see how the theory of Coxeter groups can be used to provide some answers. The talk will be of a fairly elementary nature.

To begin viewing slides, click on the first slide below.

For more on this subject try these papers:

- Coxeter Groups and Hyperbolic Manifolds by Brent Everitt
- The Smallest Hyperbolic 6-manifolds by Brent Everitt, John Ratcliffe and Steve Tschantz.
- Constructing Hyperbolic Manifolds by Brent Everitt and Colin Maclachlan.

© 2004 Brent Everitt

bje1@york.ac.uk