### School of Mathematics and Statistics

### Richard Kane

University of Western Ontario

### Lie Groups and p-Compact Groups

**Friday 23rd March, 12-1pm,
Carslaw 159. **

Algebraic topologists have studied connected compact Lie groups for
the past sixty years. One early success was to establish a clear
connection between the homology of a Lie group and its Weyl group.
This study also made clear that the classifying space of a Lie group
could be used to formulate a great deal of information about the
group and its homology. It has been a long standing question as to
just what information could be so formulated.

These considerations have lead to the creation, for each prime
*p*, of a theory of p-compact groups. Basically one is studying
connected compact Lie groups via their classifying spaces but in a
more general setting, relying on a few key properties. The pattern
obtained both incorporates and generalizes the classification of
semi-simple Lie groups. Rather than being based on Weyl groups the
pattern is based on p-adic reflection groups.

I will try to explain the above remarks keeping clear of technical
issues.