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Cheeger–Gromoll
splitting theorem for groups
Thang Nguyen and Shi Wang |
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Algebraic & Geometric Topology 22 (2022) 3377–3399
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Abstract |
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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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Keywords
Ricci curvature, conjugation curvature, Cheeger–Gromoll,
splitting, exponential growth
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Mathematical Subject Classification
Primary: 51F99
Secondary: 20E34
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References |
Publication
Received: 8 July 2020
Revised: 9 August 2021
Accepted: 5 October 2021
Published: 30 January 2023
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Authors |
| Thang Nguyen | |
| Florida State University Tallahassee, FL United States |
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| Shi Wang | |
| ShanghaiTech University Shanghai China |
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