The full holonomy group under the Ricci flow

TL;DR

This paper proves that the full holonomy group of a Ricci flow solution remains invariant up to isomorphism, utilizing the invariance of the reduced holonomy, providing a concise and direct proof.

Contribution

It offers a new, straightforward proof of the invariance of the full holonomy group under Ricci flow, emphasizing the role of reduced holonomy.

Findings

Full holonomy group is invariant under Ricci flow

Reduced holonomy invariance implies full holonomy invariance

Provides a concise proof of holonomy invariance

Abstract

We give a short, direct proof that the full holonomy group of a solution to the Ricci flow is invariant up to isomorphism using the invariance of the reduced holonomy under the flow.