  A recent result of Bader, Gelander and Sauer shows that for manifolds of
pinched negative curvature, the torsion part of the homology can be controlled
by the volume. This is done by constructing an efficient simplicial model of
the thick part, which also provides another proof of the analogous statement
for the free part of the homology, a classical theorem due to Gromov.
  We will extend these results to more general curvature conditions, namely the
case where the sectional curvature can get arbitrarily close to zero, but the
visibility axiom still holds.
