  By recent work on some conjectures of Pillay, each definably compact group in
a saturated o-minimal structure is an expansion of a compact Lie group by a
torsion free normal divisible subgroup, called its infinitesimal subgroup. We
show that the infinitesimal subgroup is cohomologically acyclic. This implies
that the functorial correspondence between definably compact groups and Lie
groups preserves the cohomology.
