  We briefly introduce the theory of perverse sheaves with special attention to
the topological situation where strata can have odd dimension. This is part of
a project to use perverse sheaves on the topological reductive Borel-Serre
compactification of a Hermitian locally symmetric space as a tool to study
perverse sheaves on the Baily-Borel compactification, a projective algebraic
variety. We sketch why the decomposition theorem holds for the natural map
between the reductive Borel-Serre and the Baily-Borel compactifications. We
demonstrate how to calculate extensions of simple perverse sheaves on the
reductive Borel-Serre compactification and illustrate with the example of
Sp(4,R).
