Cheeger–Gromoll splitting theorem for groups

Nguyen, Thang; Wang, Shi

doi:10.2140/agt.2022.22.3377

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Cheeger–Gromoll splitting theorem for groups

Thang Nguyen and Shi Wang

Algebraic & Geometric Topology 22 (2022) 3377–3399

DOI: 10.2140/agt.2022.22.3377

Abstract

We study a notion of curvature for finitely generated groups which serves the role of Ricci curvature for Riemannian manifolds. We prove an analog of the 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.

Keywords

Ricci curvature, conjugation curvature, Cheeger–Gromoll, splitting, exponential growth

Mathematical Subject Classification

Primary: 51F99

Secondary: 20E34

References

Publication

Received: 8 July 2020

Revised: 9 August 2021

Accepted: 5 October 2021

Published: 30 January 2023

Authors

Thang Nguyen
Florida State University Tallahassee, FL United States

Shi Wang
ShanghaiTech University Shanghai China

Volume 22, issue 7 (2022)