On the Fundamental Group of Non-Collapsed Ancient Ricci Flows (Journal of Mathematical Study, 2025)
We show that any manifold admitting a non-collapsed, ancient Ricci flow must have finite fundamental group. This generalizes what was known for $κ$-solutions in dimensions 2, 3. We furthermore show that this fundamental group must be a quotient of the fundamental group of the regular part of any tangent flow at infinity.
Keywords: Ricci flow; singularity model; fundamental group; kappa-solution; tangent flow