Summary: p-COMPACT GROUPS AS SUBGROUPS
OF MAXIMAL RANK OF KAC-MOODY GROUPS
In , Kitchloo constructed a map f : BX BK
p where K is a certain Kac-
Moody group of rank two, X is a rank two mod p finite loop space and f is such
that it induces an isomorphism between even dimensional mod p cohomology groups.
Here B denotes the classifying space functor and (-)
p denotes the Bousfield-Kan
Fp-completion functor ().
This space X --or rather the triple (X
p , BX
p , e) where e : X BX-- is a
particular example of what is known as a p-compact group. These objects were
introduced by Dwyer and Wilkerson in  as the homotopy theoretical framework
to study finite loop spaces and compact Lie groups from a homotopy point of view.
The foundational paper  together with its many sequels by Dwyer-Wilkerson and
other authors represent now an active, well established research area which contains
some of the most important recent advances in homotopy theory.