On the topology of manifolds with positive isotropic curvature

TL;DR

This paper proves that closed orientable manifolds with positive isotropic curvature and free fundamental group are topologically equivalent to connected sums of spheres and circles, extending understanding of manifold topology under curvature conditions.

Contribution

It establishes a classification result for high-dimensional manifolds with positive isotropic curvature and free fundamental group, linking curvature conditions to topological structure.

Findings

Manifolds with positive isotropic curvature and free fundamental group are homeomorphic to connected sums of S^{n-1} imes S^1.

The result applies to manifolds of dimension n ≥ 5.

Provides a topological classification under curvature and fundamental group constraints.

Abstract

We show that a closed orientable Riemannian $n$-manifold, $n \ge 5$, with positive isotropic curvature and free fundamental group is homeomorphic to the connected sum of copies of $S^{n-1} \times S^1$.