# Members & Former Members

## Project

15Spaces and Moduli Spaces of Riemannian Metrics with Curvature Bounds on compact and non-compact Manifolds

## Publications within SPP2026

In this article, we are interested in the question whether any complete contractible 3-manifold of positive scalar curvature is homeomorphic to $$\mathbb{R}^3$$. We study the fundamental group at infinity, $$\pi^\infty_1$$, and its relationship with the existence of complete metrics of positive scalar curvature. We prove that a complete contractible 3-manifold with positive scalar curvature and trivial $$\pi_1^\infty$$ is homeomorphic to $$\mathbb{R}^3$$.