Cheeger-Gromoll Splitting Theorem for groups
Group Theory
2023-02-15 v3 Geometric Topology
Metric Geometry
Abstract
We study a notion of curvature for finitely generated groups which serves as a role of Ricci curvature for Riemannian manifolds. We prove an analog of Cheeger-Gromoll splitting theorem. As a consequence, we give a geometric characterization of virtually abelian groups. We also explore the relation between this notion of curvature and the growth of groups.
Cite
@article{arxiv.1910.05822,
title = {Cheeger-Gromoll Splitting Theorem for groups},
author = {Thang Nguyen and Shi Wang},
journal= {arXiv preprint arXiv:1910.05822},
year = {2023}
}
Comments
20 pages, 2 figures. Minor changes, final version to appear in Algebr. Geom. Topol