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Summary: COHOMOLOGY OF CLASSIFYING SPACES OF CENTRAL
QUOTIENTS OF RANK TWO KAC-MOODY GROUPS
JAUME AGUAD´E, CARLES BROTO, NITU KITCHLOO, AND LAIA SAUMELL
Abstract. This paper is devoted to the computation of the mod p cohomology
of the classifying spaces of the quotients of (non-afine) Kac-Moody groups of rank
two by finite central p-groups, as algebras over the Steenrod algebra and higher
Bockstein operations. To this aim we enlarge the class of spaces by including some
homotopy theoretic constructions in such a way that the new class of spaces is
nicely parametrized by the integral p-adic representations of the infinite dihedral
group in rank two. Furthermore, we show how these representations encode enough
information in order to determine the mod p cohomology and Bockstein spectral
sequence of this class of spaces.
The goal of this paper is to compute the mod p cohomology algebra --including the
action of the Steenrod algebra and the Bockstein spectral sequence-- of the classifying
spaces of the quotients of (non-afine) Kac-Moody groups of rank two by finite central
p-groups.
The wise have taught us (cf. Ithaca in [6]) that in the trips which are really worth
doing what we see and learn along the trip always turns out to become more important
than the final destination. We think that the present work might be an example of
this. The rank two Kac-Moody groups have a large family of central subgroups
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