Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth Have Finitely Generated Fundamental Groups

Abstract

In this paper, we generalize the finite generation result of Sormani to non-branching $RCD(0,N)$ geodesic spaces (and in particular, Alexandrov spaces) with full support measures. This is a special case of the Milnor's Conjecture for complete non-compact $RCD(0,N)$ spaces. One of the key tools we use is the Abresch-Gromoll type excess estimates for non-smooth spaces obtained by Gigli-Mosconii.

11 pages, revised: Remark 1.5 regarding Alexandrov spaces and a reference added to the paper

References in corpus (2)

• The splitting theorem in non-smooth context
• Non-branching geodesics and optimal maps in strong CD(K,{\infty})-spaces