Deforming 3-manifolds of bounded geometry and uniformly positive scalar curvature (Q2659432)

Summary: 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 generalises the main result of the fourth author [Ann. Math. (2) 176, No. 2, 815--863 (2012; Zbl 1319.53028)] 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.