  A central theme in Riemannian geometry is understanding the relationships
between the curvature and the topology of a Riemannian manifold. Positive
isotropic curvature (PIC) is a natural and much studied curvature condition
which includes manifolds with pointwisequarter-pinched sectional curvatures and
manifolds with positive curvature operator. By results of Micallef and Moore
there is only one topological type of compact simply connected manifold with
PIC; namely any such manifold must be homeomorphic to the sphere. On the other
hand, there is a large class of nonsimply connected manifolds with PIC. An
important open problem has been to understand the result in this direction. We
show that the fundamental group of a compact manifold M^n with PIC, n geq 5,
does not contain a subgroup isomorphic to \mathbb{Z} \oplus \mathbb{Z}. The
techniques used involve minimal surfaces.
