Topological Rigidity and Positive scalar curvature

TL;DR

This paper proves that any complete, contractible 3-manifold with non-negative scalar curvature is topologically equivalent to Euclidean 3-space, linking geometric curvature conditions with topological rigidity.

Contribution

It establishes a topological rigidity result for 3-manifolds under scalar curvature constraints, extending understanding of geometric-topological interplay.

Findings

Complete contractible 3-manifolds with non-negative scalar curvature are homeomorphic to R^3.

The result connects scalar curvature positivity with topological classification.

Provides new insights into the structure of 3-manifolds under curvature conditions.

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 $\mathbf{R}^3$.