The fundamental group of manifolds of positive isotropic curvature and surface groups

Abstract

In this article, we study the topology of compact manifolds with positive isotropic curvature (PIC). There are many examples of nonsimply connected compact manifolds with PIC. We prove that the fundamental group of a compact Riemannian manifold of dimension at least $5$ with PIC does not contain a subgroup isomorphic to the fundamental group of a compact Riemann surface. The proof uses stable minimal surface theory