On the Fundamental Group of Non-Collapsed Ancient Ricci Flows

Abstract

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