Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature

Laurent Bessières, Gérard Besson, Sylvain Maillot, Fernando Coda Marques, Laurentbessì Eres, Fernando Marques

Published 2017-11-07Version 1

We prove that the moduli space of complete Riemannian metrics of bounded geometry and uniformly positive scalar curvature on an orientable 3-manifold is path-connected. This generalizes the main result of the fourth author [Mar12] in the compact case. The proof uses Ricci flow with surgery as well as arguments involving performing infinite connected sums with control on the geometry.