  In this paper we study the topology of compact manifolds of positive
isotropic curvature (PIC). There are many examples of non-simply connected
compact manifolds with positive isotropic curvature. We prove that the
fundamental group of a compact Riemannian manifold with PIC, of dimension
greater than or equal to 5, does not contain a subgroup isomorphic to the
fundamental group of a compact Riemann surface. The proof uses stable minimal
surface theory.
