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arXiv · 1910.05822

Cheeger-Gromoll Splitting Theorem for groups

Thang Nguyen·Shi Wang
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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.

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BibTeXRIS

Thang Nguyen, Shi Wang. 2019-10-13. Cheeger-Gromoll Splitting Theorem for groups. https://doi.org/10.2140/agt.2022.22.3377

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