Stephan Stadler

CAT(0) manifolds

In the early eighties, Gromov asked if a topological manifold which supports a metric of non-positive curvature in a synthetic sense has to be homeomorphic to the Euclidean space. In the talk, I will discuss Gromov's question and report on the following result obtained jointly with Alexander Lytchak and Koichi Nagano: 4-dimensional CAT(0) manifolds are homeomorphic to the Euclidean space.