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

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

2005-06-29

arxiv.org/abs/math/0506609v1

Mathematics

Differential Geometry

Scientific paper

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.

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