Blurb
We will discuss the guiding examples in the theory of infinite discrete
groups:
 arithmetic and Sarithmetic groups in characteristic 0, in
particular Sl_{n}(Z)
 Sarithmetic 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 CWcomplex).
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.
