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Cheeger–Gromoll splitting theorem for groups

Thang Nguyen and Shi Wang

Algebraic & Geometric Topology 22 (2022) 3377–3399

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.

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Ricci curvature, conjugation curvature, Cheeger–Gromoll, splitting, exponential growth
Mathematical Subject Classification
Primary: 51F99
Secondary: 20E34
Received: 8 July 2020
Revised: 9 August 2021
Accepted: 5 October 2021
Published: 30 January 2023
Thang Nguyen
Florida State University
Tallahassee, FL
United States
Shi Wang
ShanghaiTech University