2017/12/17 by Richard H. Bamler, Bruce Kleiner, Bamler, Richard H. +1
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1712.06197
openalex publication_date 2017/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We complete the proof of the Generalized Smale Conjecture, apart from the case of RP3, and give a new proof of Gabai's theorem for hyperbolic 3-manifolds. We use an approach based on Ricci flow through singularities, which applies uniformly to spherical space forms other than S3 and RP3 and hyperbolic manifolds, to prove that the moduli space of metrics of constant sectional curvature is contractible. As a corollary, for such a 3-manifold X, the inclusion Isom (X,g)→ Diff(X) is a homotopy equivalence for any Riemannian metric g of constant sectional curvature.