HYPERBOLIC GEOMETRY AND MAPPING CLASS GROUPS

Course Description

In topology the mapping class group of a surface, (sometimes called the modular group or Teichmüller modular group), is the group of homeomorphisms of the surface viewed up to continuous deformation. It is of fundamental importance for the study of 3-manifolds and various other areas of mathematics. I'll give a gentle introduction to the classification of mapping classes which will be used as an excuse to tramp around in various areas of low-dimensional topology.