RCD(0,N)-spaces with small linear diameter growth

TL;DR

This paper investigates the structure of the fundamental group in RCD(0,N) spaces, showing it is finitely generated under small linear diameter growth, extending classical results from Riemannian geometry.

Contribution

It generalizes Sormani's results to RCD(0,N) spaces, establishing finite generation of the fundamental group with small linear diameter growth.

Findings

Revised fundamental group is finitely generated under small linear diameter growth.

Generalizes classical Riemannian results to metric measure spaces.

Extends understanding of geometric group properties in non-smooth spaces.

Abstract

In this paper, we study some structure properties on the (revised) fundamental group of RCD(0,N) spaces. Our main result generalizes earlier work of Sormani on Riemannian manifolds with nonnegative Ricci curvature and small linear diameter growth. We prove that the revised fundamental group is finitely generated if assuming small linear diameter growth on RCD(0,N) spaces.