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

Yu Kitabeppu; Sajjad Lakzian

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

Metric Geometry 2018-07-24 v2

Authors: Yu Kitabeppu , Sajjad Lakzian

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.

Keywords

rcd(0,n) spaces fundamental group finite generation non-branching geodesic spaces alexandrov spaces abresch-gromoll inequality milnor's conjecture

Cite

@article{arxiv.1405.0897,
  title  = {Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth Have Finitely Generated Fundamental Groups},
  author = {Yu Kitabeppu and Sajjad Lakzian},
  journal= {arXiv preprint arXiv:1405.0897},
  year   = {2018}
}

Comments

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

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

Abstract

Keywords

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