A bound for the order of the fundamental group of a complete noncompact Ricci shrinker

TL;DR

This paper provides a quantitative bound on the order of the fundamental group of complete noncompact Ricci shrinkers, extending previous results that established finiteness.

Contribution

It introduces a specific bound for the fundamental group's order in complete noncompact Ricci shrinkers, advancing understanding of their topological properties.

Findings

Fundamental group of Ricci shrinkers is finite.

Established an explicit bound on the order of the fundamental group.

Extended Wylie's finiteness result with quantitative estimates.

Abstract

For complete shrinking (gradient) Ricci solitons, we observe a quantification of Wylie's result that the fundamental group is finite.