Topology Seminar: Alejandro Adem (UBC)

In this talk we will discuss properties of spaces of homomorphisms Hom(Q,G) where Q is a discrete group and G a Lie group. The example given by the ordered commuting n-tuples in a compact Lie group will be explained in some detail. We will discuss how spaces of homomorphisms and the descending central series of the free groups can be used to construct a filtration of the classifying space BG. Homotopy properties of these constructions will be given for finite groups, and cohomology calculations provided for compact Lie groups. We will also describe results on understanding both the number and stable homotopy type of the components of related spaces of representations.