### CAT(0) manifolds

Analysis and Geometry Seminar

10th February 2022, 3:15 pm – 4:15 pm

Online, Contact organisers for details

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.

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