  A class of abelian fibered Calabi-Yau threefolds X_{m,n} is shown yield SU(2)
structure, in addition to the standard SU(3) holonomy. Compactification of type
II string theory on a manifold in this class give a 4D effective supergravity
theory in which the topology spontaneously breaks N=4 to N=2 supersymmetry. The
breaking occurs at a scale hierarchically lower than the compactification scale
when the P^1 base is large compared to the T^4 fiber. We analyze the moduli
space of SU(2) structure metrics of the N=4 theory and its restriction to the
moduli space of Calabi-Yau metrics of the N=2 theory, showing that the latter
agrees with the expectation computed from triple intersection numbers in the
classical limit. Finally, we analyze the twisted cohomology ring associated
with the SU(2) structure of X_{m,n} and show that the breaking of N=4 to N=2 is
conveniently summarized in the lifting cohomology classes as one passes to the
standard cohomology ring, with massive modes persisting as torsion classes when
the coupling is nonminimal. The analysis is facilitated by the existence of
explicit first-order metrics obtained by classical supergravity dualities.
