Math 739 - Important Groups

Instructor:  Kai-Uwe Bux
Time:  MWF 12:20-13:10
Room:  205 MT
Office hours:  MW 13:30-14:30
Office:  583 MT


To be proof read


We will discuss the guiding examples in the theory of infinite discrete groups:

  • arithmetic and S-arithmetic groups in characteristic 0, in particular Sln(Z)
  • S-arithmetic groups in positive characteristic
  • mapping class groups of surfaces
  • (outer) automorphism groups of free groups
  • Thompson's groups
  • groups of tree automorphisms, in particular Grigorchuk's group.

These groups are important in the sense that if someone presents a new technique it is considered interesting if it adds to our knowledge about one of these groups: these are groups about which mathematicians want to know everything.

A more or less unifying theme in this class will be the idea that you can study a group by means of a nice action of the group (e.g., an action with small stabilisers) on a nice space (e.g., a highly connected CW-complex). We will emphasise this interplay of topology and group theory.

Prerequisites: Algebra (631) and some advanced Topology (e.g.: 651). Basically you should know groups and actions, fundamental groups of spaces and covering spaces; the concepts of homology and homotopy should ring a bell.

To view or print the pdf-files, you might need the acrobat reader, which is available free of charge.