Topological Rigidity and Positive scalar curvature

Abstract

In this paper, we study the topological rigidity and its relationship with the positivity of scalar curvature. Precisely, we show that any complete contractible $3$-manifold with non-negative scalar curvature is homeomorphic to ${\mathbf{R}}^3$.

The proof of Lemma 7.8 is incomplete

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Contractible $3$-manifold and Positive scalar curvature (I)