Contractibility of open Ric_2-manifolds with positive asymptotic volume ratio

Determine whether every open Riemannian manifold with Ric_2 ≥ 0 and positive asymptotic volume ratio is contractible.

Background

The proven theorem gives vanishing of homology in degrees at least 3 for open manifolds with Ric_2 ≥ 0 and positive asymptotic volume ratio, but contractibility is substantially stronger than homological triviality.

The question is motivated by the fact that the corresponding statement holds for nonnegative sectional curvature and positive asymptotic volume ratio, and is known affirmatively in dimension 3 for Ric_2 ≥ 0. It remains unresolved in general.

References

When $k=2$, we can additionally ask whether Theorem \ref{T:open_mfs} can be improved even further in the following sense. Are all open Riemannian manifolds of $Ric_2\geq 0 $ and $\alpha>0$ contractible?

— Local Topology of Riemannian Manifolds with Lower Intermediate Ricci Curvature Bounds  (2609.10268 - Reiser et al., 9 Sep 2026) in Section 1, Question 1.5 (labeled Q:open_Ric2)