On the fundamental group of non-collapsed ancient Ricci flows

TL;DR

This paper proves that manifolds with non-collapsed ancient Ricci flows have finite fundamental groups, extending previous results in lower dimensions, and relates these groups to tangent flows at infinity.

Contribution

It establishes the finiteness of the fundamental group for non-collapsed ancient Ricci flows and links it to tangent flow structures, generalizing known results.

Findings

Manifolds with non-collapsed ancient Ricci flows have finite fundamental groups.

The fundamental group is a quotient of the regular part of tangent flow groups.

Extension of known results from 2D and 3D to higher dimensions.

Abstract

We show that any manifold admitting a non-collapsed, ancient Ricci flow must have finite fundamental group. This generalizes what was known for $\kappa$-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.