  We prove a conjecture of Gromov's to the effect that manifolds with isotropic
curvature bounded below by 1 (after possibly rescaling) are macroscopically
1-dimensional on the scales greater than 1. As a consequence we prove that
compact manifolds with positive isotropic curvature have virtually free
fundamental groups. Our main technique is modeled on Donaldson's version of
H\"ormander technique to produce (almost) holomorphic sections which we use to
construct destabilizing sections.
