# What’s new on the ArXiv: Ricci flow and diffeomorphism groups of 3-manifolds

A new preprint proves the contractibility of the space of constant curvature metrics on all 3-manifolds except possibly real projective space. Bamler, Kleiner: Ricci flow and diffeomorphism groups of 3-manifolds, https://arxiv.org/pdf/1712.06197.pdf The Smale conjecture in its original form asserted that the diffeomorphism group of the 3-sphere deformation retracts onto O(3), the isometry group of its “round” constant curvature metric. It was proved by Hatcher in … Continue reading What’s new on the ArXiv: Ricci flow and diffeomorphism groups of 3-manifolds