  We give an elementary proof of the fact that a pure-dimensional closed
subvariety of a complex abelian variety has a signed intersection homology
Euler characteristic. We also show that such subvarieties which, moreover, are
local complete intersections, have a signed Euler-Poincare characteristic. Our
arguments rely on the construction of circle-valued Morse functions on such
spaces, and use in an essential way the stratified Morse theory of
Goresky-MacPherson. Our approach also applies (with only minor modifications)
for proving similar statements in the analytic context, i.e., for subvarieties
of compact complex tori. Alternative proofs of our results can be given by
using the general theory of perverse sheaves.
