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

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