CAT(0) 4-manifolds are Euclidean

TL;DR

This paper proves that any topological 4-manifold with globally non-positive curvature is topologically equivalent to Euclidean 4-space, establishing a significant geometric-topological classification result.

Contribution

It establishes that all topological 4-manifolds with non-positive curvature are homeomorphic to Euclidean space, a new classification in geometric topology.

Findings

Topological 4-manifolds with non-positive curvature are homeomorphic to Euclidean space.

The result applies to all such manifolds, regardless of additional structure.

This bridges geometric curvature conditions with topological classification in four dimensions.

Abstract

We prove that a topological 4-manifold of globally non-positive curvature is homeomorphic to Euclidean space.