Title:
Cohomology of buildings and finiteness properties of $\tilde A_n$-groups

Authors:
Jacqui Ramagge, University of Newcastle 
Wayne W. Wheeler, University of Leicester 

Abstract:
Borel and Serre calculated the cohomology of the building associated to
a reductive group and used the result to deduce that torsion-free
$S$-arithmetic groups are duality groups.  By replacing their
group-theoretic arguments with proofs relying only upon the geometry
of buildings, we show that Borel and Serre's approach can be modified
to calculate the cohomology of any locally finite affine building.  As
an application we show that any finitely presented $\tilde A_n$-group
is a virtual duality group. A number of other finiteness conditions for
$\tilde A_n$-groups are also established.

Status: Preprint