Spaces of positively curved Riemannian metrics

It is by now a classical topic in index theory to study on a (closed) Riemannian (spin) manifold the space of all Riemannian metrics of positive scalar curvature. We have several results showing that this space is usually highly complicated from a homotopy theoretic point of view (provided it is non-empty). Instead of studying positivity … Continue reading "Spaces of positively curved Riemannian metrics"

Large scale properties of 3-manifold groups

A week ago there was a preprint posted on the arXiv by Peter Haïssinsky and Cyril Lecuire about Quasi-isometric rigidity of three manifold groups (arXiv:2005.06813). Building on work by many other people, they complete the proof that the class of 3-manifold groups is quasi-isometrically rigid, meaning the following: if a finitely generated group G is quasi-isometric … Continue reading "Large scale properties of 3-manifold groups"